วารสารมหาวิทยาลัยศิลปากร by SURIC

SILPAKORN UNIVERSITY Science and Technology Journal SUSTJ

Copyright All rights reserved. Apart from citations for the purposes of research, private study, or criticism and review, no part of this publication may be reproduced, stored or transmitted in any other form without prior written permission by the publisher. Published by Silpakorn University Printing House. Silpakorn University, Sanamchandra Palace Campus, Nakhon Pathom 73000 ÂŠ Silpakorn University ISSN 1905-9159

SILPAKORN UNIVERSITY Science and Technology Journal Editorial Office Silpakorn University Research and Development Institute (SURDI), Silpakorn University, Sanamchandra Palace Campus, Nakhon Pathom, Thailand

Editorial Policy All articles submitted for publication will be evaluated by a group of distinguished reviewers. The editorial board claims no responsibility for the contents or opinion expressed by the authors of individual article.

Editorial Advisory Board Assist. Prof. Alice Thienprasert, Ph.D Director, Silpakorn University Research and Development Institute, Thailand Prof. Amaret Bhumiratana, Ph.D Department of Biotechnology, Mahidol University, Thailand Prof. Geoffrey A. Cordell, Ph.D Professor Emeritus, University of Illinois at Chicago, USA Prof. Kanaya Shiginori, Ph.D Department of Material and Life Sciences, Osaka University, Japan Prof. Keiji Yamamoto, Ph.D Graduate School of Pharmaceutical Sciences, Chiba University, Japan Assoc. Prof. Kriengsak Poonsuk, Ph.D Faculty of Animal Sciences and Agricultural Technology, Silpakorn University, Thailand Assist. Prof. Lerkiat Vongsarnpigoon, Ph.D National Metal and Materials Technology Center (MTEC), Thailand Assoc. Prof. Nijsiri Ruangrungsri, Ph.D Department of Pharmacognosy, Chulalongkorn University, Thailand Assoc. Prof. Petcharat Pongcharoensuk, Ph.D Department of Pharmacy, Mahidol University, Thailand Prof. Piyasan Praserthdam, Ph.D Department of Chemical Engineering, Chulalongkorn University, Thailand Assoc. Prof. Surachai Nimjirawath, Ph.D Department of Chemistry, Silpakorn University, Thailand Prof. Tharmmasak Sommartya, Ph.D Faculty of Agriculture, Bangkhen Campus, Kasetsart University, Thailand Prof. Virulh Sa-Yakanit, Ph.D Department of Physics, Silpakorn University, Thailand

Editor Assoc. Prof. Onoomar (Poobrasert) Toyama, Ph.D Faculty of Pharmacy, Silpakorn University

SILPAKORN UNIVERSITY Science and Technology Journal Editorial Board Assist. Prof. Bussarin Ksapabutr, Ph.D Faculty of Engineering and Industrial Technology, Silpakorn University Prof. Chawewan Ratanaprasert, Ph.D Faculty of Science, Silpakorn University Assist. Prof. Chockpisit Thepsithar, Ph.D Faculty of Science, Silpakorn University Assoc. Prof. Mana Kanjanamaneesathian, M.Appl.Sc. Faculty of Animal Sciences and Agricultural Technology, Silpakorn University Assist. Prof. Pramote Khuwijitjaru, Ph.D Faculty of Engineering and Industrial Technology, Silpakorn University Agnes Rimando, Ph.D U.S. Department of Agriculture, Agricultural Research Service, USA Prof. Juan Boo Liang, Ph.D Institute of Bioscience, Universiti Putra Malaysia, Malaysia Prof. Shuji Adachi, Ph.D Graduate School of Agriculture, Kyoto University, Japan Vincenzo Esposito, Ph.D Department of Chemical Science and Technology, University of Rome, Italy

Managing Editor Pranee Vichansvakul

Periodicity Twice yearly

All correspondence should be addressed to: Managing Editor, SUSTJ, 44/114 Soi Phaholyothin 52 Phaholyothin Road, Klongthanon, Saimai, Bangkok 10220, Thailand Telephone: 080-5996680 Fax: 66-2973-8366 E-mail address: pranee_aon1@hotmail.com Web site: http://www.journal.su.ac.th

Information about the Journal An electronic journal is provided on the web site (http://www.journal.su.ac.th). The journal is available at Silpakorn University Book Center. Telephone: 66-2223-7345, 66-2434-1792, 66-3424-4054.

Instructions to Authors Silpakorn University Science and Technology Journal (SUSTJ) is published twice a year in June and December by the Research and Development Institute of Silpakorn University, Thailand. The journal puts together articles in Science and Technology and aims to promote and distribute peer reviewed articles in the areas of science, health science, animal science, agriculture, engineering, technology and related fields. Articles from local and foreign researchers, invited articles and review from experts are welcome.

Types of contributions Short communications, Research articles, Review articles Preparation of manuscripts 1. The text should be double-spaced with line number on A4 and a font Times New Roman size 11 should be used. When using MS Word, insert all symbols by selecting “Insert-Symbol” from the menu and use the “Symbol” font. 2. Manuscripts should be organized in the following order: Cover page with title and authors’ names and affiliations Abstract (in English and Thai) Key Words Introduction Materials and Methods, Area Descriptions, Techniques Results Discussion Conclusion Acknowledgements References Tables and Figures Authors’ names and affiliations Full names and affiliations (marked with superscript number) should be provided for all authors on the cover page, separately from the content. The corresponding author (marked with superscript asterisk) should also provide a full postal address, telephone and fax number and an e-mail address as a footnote on the title page. Abstract First page of the content starts with Abstract, including title of the article on top of page. Provide a short abstract not more than 200 words, summarizing the question being addressed and the findings. Key Words Provide 3-5 key words or short phrases in alphabetical order, suitable for indexing. References In text references: Refer to the author’s name (without initials) and year of publication, e.g., Feldmann, 2004 (for 1 author), Feldmann and Langer, 2004 (for 2 authors), or Feldmann et al., 2004 (for more than 2 authors). Article references: References should be listed in alphabetical order of author(s). For journal, list all names of authors. Book Feldmann, H. (2004) Forty Years of FEBS, 2nd ed., Blackwell Publishing Ltd., Oxford.

Chapter in a book Langer, T. and Neupert, W. (1994) Chaperoning mitochondrial biogenesis. In The Biology of Heat Shock Proteins and Molecular Chaperones (Morimoto, R. I., Tissieres, A. and Georgopoulos, C., eds.), 3rd ed., pp. 53-83. Cold Spring Harbor Laboratory Press, Plainview, New York. Article in a journal Hammerschlag, F. A., Bauchan, G., and Scorza, R. (1985) Regeneration of peach plants from callus derived from immature embryos. Journal of Natural Products 70(3): 248-251. Hammerschlag, F. A., Bauchan, G., and Scorza, R. Regeneration of peach plants from callus derived from immature embryos. Journal of Natural Products (in press). Article on the web Lee, K. (1999) Appraising adaptaive management. Conservation Ecology 3(2). [Online URL:www. consecolo.org/Journal/vol3/iss2/index.html] accessed on April 13, 2001. Proceedings MacKinnon, R. (2003) Modelling water uptake and soluble solids losses by puffed breakfast cereal immersed in water or milk. In Proceedings of the Seventh International Congress on Engineering and Food, Brighton, UK. Patent Yoshikawa, T. and Kawai, M. (2006) Security robot. U.S. Patent No. 2006079998. Tables and Figures Each Table and Figure must be on a separate page of the manuscript. Tables: Number the tables according to their sequence in the text. The text should include references to all tables. Vertical lines should not be used to separate columns. Leave some extra space instead. Figures: Figures should be of high quality (not less than 300 dpi JPEG or TIFF format), in black and white only, with the same size as the author would like them to appear in press. Choose the size of symbols and lettering so that the figures can be reduced to fit on a page or in a column. Submission of Manuscripts Authors should verify, on the submission form, that the submitted manuscript has not been published or is being considered for publication elsewhere. All information contained in an article is full responsibility of the authors, including the accuracy of the data and resulting conclusion. Authors are requested to send the manuscript on a CD labeled with the authors’ names and file names. The files should be prepared using MS Word only. Three copies of manuscript must be supplied. The editorial office will acknowledge receipt of the manuscript within 2 weeks of submission. The ‘accepted date’ that appears in the published article will be the date when the managing editor receives the fully revised version of the manuscript. The manuscript may be returned to authors for revision. Authors will be given 2 weeks after receipt of the reviewers’ comments to revise the article.

Please submit the manuscript with a CD and a submission form to the following address: Pranee Vichansvakul 44/114 Soi Phaholyothin 52 Phaholyothin Road, Klongthanon, Saimai, Bangkok 10220

Proofs Proofs will be sent to the corresponding author by e-mail (as PDF file) or regular mail. Author is requested to check the proofs and return any corrections within 2 weeks.

Silpakorn University Science and Technology Journal

Contents

Volume 6 Number 1 (January - June) 2012

Invited Article

Green Pharmaceutical Chemistry for the Sustainability …………...………………......……………………........………………………...

Theerasak Rojanarata

Review Article

The Estimation of Smoothing Parameter using Smoothing Techniques on

Nonparametric Regression…………...………………………………………......................………………………........………………………........………………………...

Autcha Araveeporn

Research Articles

Confidence Intervals for the Parameter of a Gaussian First-Order Autoregressive Model

with Additive Outliers: A Simulation Study…………………………………......................………………………........………………………...........……

Wararit Panichkitkosolkul, Luckhana Saothayanun, Yupin Kanjanasakda and

Sunee Taweesakulvatchara

Preparation of Pectin from Fruit Peel of Citrus maxima……………...…………………................................................................................

Uthai Sotanaphun, Amornrut Chaidedgumjorn, Nudchanart Kitcharoen,

Malai Satiraphan, Panida Asavapichayont and Pornsak Sriamornsak

Development of Instant Rice for Young Children..........................................................................................................................................................

Bencharat Prapluettrakul, Patcharee Tungtrakul, Sukamol Panyachan and

Tasanee Limsuwan SUSTJ is now available on the following databases: Chemical Abstract Service (CAS), International Information System for the Agricultural Sciences and Technology (AGRIS), AGRICultural Online Access (AGRICOLA) Food Science and Technology Abstracts (FSTA), Directory of Open Access Journals (DOAJ), Google Scholar, Thai Journal Citation Index Centre (TCI Centre).

Invited Article Green Pharmaceutical Chemistry for the Sustainability Theerasak Rojanarata* Department of Pharmaceutical Chemistry and Pharmaceutical Development of Green Innovations Group (PDGIG), Faculty of Pharmacy, Silpakorn University, Nakhon Pathom 73000, Thailand * Corresponding author. E-mail address: teerasak@su.ac.th Abstract As a result of current environmental crises, the awareness and cooperation from all sectors are needed to help prevent and solve the problems. In pharmaceutical chemistry discipline, attempts have been made to use the processes with the least adverse impacts on the environment. In this article, an overview of the “6-R” approach applicable to the development of greener methodologies for drug synthesis and analysis is presented and the paradigms of works are illustrated. It is also anticipated that the article will create the environmental conscience and promote the social responsibility for the development and use of eco-friendlier processes, leading to the sustainability. Key Words: Green; Environmentally friendly; Pharmaceutical chemistry; Sustainability In the era where the environment issues are increasingly concerned, two terms universally mentioned about are inevitably “green” and “sustainability”. Green chemistry, coined in 1991, is defined as “the design of chemical products and processes that reduce or eliminate the use and generation of hazardous substances”. This approach has shifted the previously used chemical methods to become more environmentally acceptable. Later, a variety of greens e.g. green energies, green vehicles, green buildings and so forth are commonly heard. The other term; sustainability is defined as: “…meeting the needs of the present without compromising the ability of future generation to meet their own needs”. At present, “green” and

“sustainable” are inseparable and have been used interchangeably because it has been accepted that green philosophy has become both a culture and a strategy for achieving the sustainability. It is not surprising that the number of scientific researches and inventions on greener processes and products have grown enormously, intending to find a more sustainable way of life. While the awareness and cooperation are urgently called for from all sectors of the society, this movement has also driven the practice and research in pharmaceutical chemistry to the greener ways. In the past, a lot of pharmaceutical processes were developed and used without delicate ecological concerns, leading to undesirable environmental

Dr. Theerasak Rojanarata has received Silpakorn University Outstanding Researcher Award in 2010, Outstanding Royal Golden Jubilee Ph.D. Alumni Award (Biosciences) in 2010, and Nagai Award Thailand (Pharmaceutical Science Research) in 2011.

Silpakorn U Science & Tech J 6 (1) : 7-13, 2012

Silpakorn U Science & Tech J Vol.6(1), 2012

Green Pharmaceutical Chemistry for the Sustainability

consequences. The goal of the new drug investigation was primarily to obtain the most pharmacologically active molecules with the highest stability. Hence, when they end up their functions leaching into the environment, some drugs persist and tend to accumulate in soil, water as well as terrestrial and aquatic organisms. In a similar way, organic chemists are customarily taught to maximize the yield of a synthesis by exhaustively incorporating reagents, operating conditions and energies into the reactions. Although this is a reasonable goal and an effective measure of the efficiency of a particular reaction, it may not be a good achievement index in the aspect of atom economy and sustainability. In the pharmaceutical analysis, the development of analytical methods has paid attention on the optimization of critical parameters e.g. accuracy, precision, sensitivity, simplicity, cost and speed. However, other aspects concerning operator safety and environmental impact of the methods are not commonly considered. Accordingly, it is a fact that in some circumstances the chemicals employed for the analysis are even more toxic than species being determined. By the aforementioned reasons, the development of pharmaceutical processes by merging suitable technologies with environmental safety is more concerned nowadays and is one of the key challenges of the millennium. Among various green strategies to move towards sustainability, our group namely “Pharmaceutical Development of Green Innovations Group (PDGIG)” has established the “6-R” approach for the development of pharmaceutical processes. According to this rationale, the research and development should be “relevant” to the real problems and should employ “reachable” technologies; in other words, technologies that can be practically implemented by the operators. In this sense, it can be seen that many academic researches do not meet industrial interests and applications. Too sophisticated technology with high cost of instrument acquisition, operation and maintenance

may become deterrents which hinder the adoption of greener methods coming from the research base. To break these barriers down, collaborative research between researchers and practitioners will become a solution. Also, simplicity not complexity of the method should be born in mind to help bridge the gap between academia and industry and to facilitate the technology transfer. In technical aspect, toxic chemicals or harmful procedures should be “replaced”. This can be done by the development of new safer methodologies or the modification of existing processes using safer reagents. However, the complete substitution of toxic reagents is always not an easy task. The “reduction” of the reagent use and waste generation should be considered. In this respect, downscaling of the methods, the use of modern analytical techniques with breakthroughs in microelectronics, miniaturization and the combination with chemometrics allow the development of the assays with reagent-saving features. This strategy not only benefits the environment and operators as a result of reduced risk of exposure to the hazardous reagents, but also saves costs on chemical purchase and waste management. Furthermore, this approach is encouraged and useful in the context of education. Substitution of old large scale experimental practices by attractive downsized procedures will result in the immediate reduction of wastes as well as developing the environmental conscience essential for our students in the future. Once eco-friendlier methods have been proposed, it must be ascertained that they “remain” satisfactory in performance. For example, the accuracy and precision of the analytical methods must meet the prerequisites when the analysis is miniaturized. The extraction efficiency should not be lowered after previously used extractants are substituted by alternative benign solvents. Lastly, the method should be “responsible” for the environment. Answers must be ready for a simple question such as “Can we safely release the wastes 8

T. Rojanarata

Silpakorn U Science & Tech J Vol.6(1), 2012

aminotransferase, an enzyme originally isolated from soil bacteria in Thailand, for the synthesis of d-phenylglycine, an unnatural amino acid used as a side chain for the anti-infective drugs ampicillin and cephalexin (Rojanarata et al., 2004). The developed method was straightforward, requiring one-step reaction and inexpensive precursors. Toxic chemicals e.g. hydrogen cyanide which are employed in the traditional racemic resolution were no longer used. Importantly, the satisfactory yield with high enantiopurity was obtained. For the drug analysis, we have applied this enzyme for the development of a new assay for amoxicillin in the pharmaceutical preparations (Rojanarata et al., 2010). In this method, the drug was selectively converted by penicillin acylase and d -phenylglycine aminotransferase to the product 4-hydroxybenzoylformate with strong ultraviolet light absorption (Figure 1). The amount of amoxicillin was thus determined as an increase of absorbance by using spectrophotometers which were commonly available in the laboratories. The assay was found to be linear and sensitive. The accuracy, precision and specificity of the assay were satisfactory and comparable to the pharmacopoeial method which was based on high performance liquid

from the process to the environment?â&#x20AC;? Basically, the guidance for the waste management should be provided together with the protocol of developed method. More efficiently, additional efforts may be made by the recovery of reagents towards achieving zero emission or by on-line decontamination of wastes. We illustrate here some examples of greener alternatives for the pharmaceutical processes which have been developed by our group. Enzyme-based pharmaceutical processes Enzyme catalysis has several characteristics that are relevant to the green chemistry. Enzymes speed up the rates of reactions with high degree of chemo-, stereo- and regio- specificity. Therefore the enzyme-based drug synthesis and analysis offer faster throughput, possibility of asymmetric synthesis and satisfactory analyte selectivity. In addition, their water solubility and natural operation under mild to moderate conditions offer the opportunity for the reactions to take place in aqueous medium without the use of organic solvents or extreme pH, temperature, etc. Because of these advantages over non-catalyzed and chemically catalyzed reactions, we have exploited d -phenylglycine

Figure 1 Novel assay for amoxicillin in the pharmaceutical preparations based on enzymatic reactions and spectrophotometry

Silpakorn U Science & Tech J Vol.6(1), 2012

Green Pharmaceutical Chemistry for the Sustainability

chromatography (HPLC). In the environmental view points, all procedures were free from the use of organic solvents or hazardous chemicals which were detrimental to the environment and had a low consumption of reagents. In addition, the antimicrobial activity of drug samples was enzymatically inactivated prior to waste disposal, therefore the inappropriate release of the antibiotic into the environment and the occurrence of drug resistance were lower. Thus, the method was safe for the operators and eco-friendly.

To further broaden the application of enzymes to the isolation of natural products, we have employed plant cell wall-degrading enzymes i.e. cellulase, hemicellulase and pectinase for the enzyme-assisted extraction of active constituents from Thai herbal plants such as the extraction of oil from Plai (Zingiber Cassumunar Roxb.) (Figure 2) (Chuchote et al., 2009). The results showed that the incorporation of enzymatic treatment of plant materials prior to the extraction process yielded a higher content of a-terpinen-4-ol, the

Figure 2 Enzyme-assisted extraction of Plai oil using plant cell wall-degrading enzymes pharmacologically active compound in Plai oil, than that obtained from the ethanol extraction method without the enzymatic treatment. This finding demonstrates that the enzyme helps break down the cell walls and facilitates the release of oil, leading to the enhanced extraction efficiency.

are their ozone depletion properties, the global warming potential resulting from the production of photochemical smog and the environmental persistence. For these reasons, a number of strategies for solvent replacement have been investigated including the use of benign non-volatile organic solvents, water under superheated conditions, supercritical fluids, renewable solvents, ionic liquids, etc. Acetonitrile is ranked as a toxic chemical as in liquid or vapor and waste has to be detoxified through special chemical treatment, leading to high to very high disposal cost. Methanol is also toxic to humans and causes adverse effects on aquatic life. Since both solvents are most commonly used in reversed phase HPLC, we have developed an alternative method for the stability-indicating assay

Chromatographic methods using greener mobile phases Organic solvents and volatile organic compounds (VOCs) are currently used in almost all pharmaceutical processes e.g. drug synthesis, extraction, recrystallization, dissolution of solids and chromatographic separation. Besides the adverse health effects such as dizziness, irritation and carcinogenicity, the main environmental concerns related to these solvents especially VOCs

T. Rojanarata

Silpakorn U Science & Tech J Vol.6(1), 2012

Miniaturized titrations for the analysis of sodium chloride and basic drugs as hydrochloride salts Classical methods such as titrations are still the methods of choice for the assays of many pharmaceutical bulk materials and some preparations because of their simplicity, cost and speed of operation. However, one of the drawbacks is the large size of the analysis, resulting in a large amount of reagents consumed and wastes generated. To solve these problems, we have designed a miniaturized titration using Volhardâ&#x20AC;&#x2122;s agentimetric titration for the assay of sodium chloride as a model (Rojanarata et al., 2011a). The reactions were downscaled to less than 2 mL and were carried out in microcentrifuge tubes using micropipettes for the transfer of reagents. The assay started with the precipitation of chloride with a measured excess of silver nitrate. The unreacted silver nitrate left in the supernatant was separated from the precipitate by centrifugation, transferred to a new set of tubes and then titrated with different volumes of standard ammonium thiocyanate solution. The equivalence point was determined based on a photometric titration by the absorbance measurement at 450 nm to diminish human visual errors, using microplate reader which quickened multi-sample measurements

of prednisolone in tablets using eco-friendlier ethanol-water mobile phase (Rojanarata, 2011). In the environmental considerations, ethanol is acknowledged as green because of its biomass origin e.g. from agricultural feedstock and its biodegradability. Additionally, it is less harmful to human as well as the environment and requires less expensive and easier waste management. From our study, the chromatographic analysis of prednisolone was achieved on the C18 column at 50 Â°C, using a 30:70 ethanol-water as the mobile phase with the flow rate of 0.8 mL min-1. There was no interference from the background absorption of the mobile phase as well as the problems related to the back pressure generated in the system. The peak of prednisolone was well resolved from various degradation products as well as the tablet excipients at the retention time of about 10 min. In addition, statistical analysis confirmed that the assay results obtained from the proposed method were not significantly different from those obtained from the British Pharmacopoeia method which used methanol and water (42:58) as the mobile phase. Therefore, the proposed method was proven an effective alternative assay in the aspect of both analytical performance and sustainable viewpoint.

Figure 3 Miniaturized titration for the assay of sodium chloride which saves the reagent consumption and reduces waste generation while remaining the satisfactory analytical performance

Silpakorn U Science & Tech J Vol.6(1), 2012

Green Pharmaceutical Chemistry for the Sustainability

indeed hopeful that the think green culture will happen in all professions and generations and the environmental awareness is created among the mass of people, taking all of us to the sustainable future.

(Figure 3). After testing with NaCl raw material, NaCl tablets, NaCl intravenous infusion and NaCl and glucose intravenous infusion, the downsized method showed good accuracy comparable to the British Pharmacopoeial large-scale method and gave satisfactory precision (intra-day, inter-day, between-analyst and between-pipette model) with the relative standard deviation of less than 1%. In addition, the method was found to be faster in the case of multi-sample analysis. The amount of the reagents consumed in the miniaturized titration was significantly reduced by 25 - 215 folds, while the release of solid wastes was drastically reduced at about 25 fold. The use of noxious and environmentally harmful dibutyl phthalate was absolutely eliminated in the proposed method. Based on the same principle of chloride determination, the developed method was further applied for the assay of basic drugs which were often prepared as hydrochloride (HCl) salts. Nowadays, most pharmacopoeial assays of their bulk materials are acid-base titrations in non-aqueous solvents in which harsh, unsafe chemicals such as glacial acetic acid, acetic anhydride and mercury(II) acetate are usually employed. Using phenylpropanolamine HCl and metformin HCl raw materials as model analytes, it was found that the miniaturized photometric Volhardâ&#x20AC;&#x2122;s method gave accurate and precise analytical results (Rojanarata et al., 2011b). Importantly, it was safe for the analysts by the elimination of undesirable or dangerous chemicals and was friendly to the environment by lower the release of toxic wastes.

Acknowledgements The author acknowledges the financial supports of the Department of Environmental Quality Promotion, Ministry of Natural Resources and Environment and Faculty of Pharmacy, Silpakorn University, Thailand which enable us (Pharmaceutical Development of Green Innovations Group) to do the green researches as well as educational and social activities. References Chuchote, T., Opanasopit, P., and Rojanarata, T. (2009) Enzyme-assisted extraction of Plai (Zingiber cassumunar. Roxb.) In Proceedings of the 35th Congress on Science and Technology of Thailand, Chonburi, Thailand. Rojanarata, T. (2011) Eco-friendly, operator-safe and cost-effective RP-HPLC method for stability-indicating assay of prednisolone tablets using ethanol-water as mobile phase. International Journal of Pharmacy and Pharmaceutical Sciences. Accepted manuscript. Rojanarata, T., Isarangkul, D., Wiyakrutta, S., Meevootisom, V., and Woodley J. M. (2004) Controlled-release biocatalysis for the synthesis of D-phenylglycine. Biocatalysis and Biotransformation 22 (3): 195-201. Rojanarata, T., Opanasopit, P., Ngawhirunpat, T., Saehuan, C., Wiyakrutta, S., and Meevootisom, V. (2010) A simple, sensitive and green bienzymatic UV-spectrophotometric assay of amoxicillin formulations. Enzyme and Microbial Technology 46: 292â&#x20AC;&#x201C;296. Rojanarata, T., Sumran, K., Nateetaweewat, P., Winotapun, W., Sukpisit, S., Opanasopit, P., and Ngawhirunpat, T. (2011a) Microscale

Conclusions Reaching to this point, it is anticipated that the reader will have concluded that green philosophy is not a new branch of sciences, but it is an approach that strengthens all of disciplines including pharmaceutical chemistry. In addition, it has inseparable technological, environmental, economic and societal goals. Therefore, it is 12

T. Rojanarata

Silpakorn U Science & Tech J Vol.6(1), 2012

chemistry-based design of eco-friendly, reagent-saving and efficient pharmaceutical analysis: a miniaturized Volhardâ&#x20AC;&#x2122;s titration for the assay of sodium chloride. Talanta 85: 1324-1329. Rojanarata, T., Waewsa-nga, K., Buacheen, P., Opanasopit, P., and Ngawhirunpat T.

(2011b) Development of greener and safer assays for hydrochloride drugs: photometric microtitration of phenylpropanolamine hydrochloride and metformin hydrochloride. Advanced Materials Research 361-363: 1892-1896.

Review Article The Estimation of Smoothing Parameter using Smoothing Techniques on Nonparametric Regression Autcha Araveeporn* Department of Applied Statistics, Faculty of Science, King Monkutâ&#x20AC;&#x2122;s Institute of Technology Ladkrabang, Thailand * Corresponding author. E-mail address: kaautcha@kmitl.ac.th Received April 22, 2011; Accepted September 12, 2011

Abstract This article discusses on the smoothing parameter which is controlled by interpolating spline based on the smoothing techniques that consisted of smoothing spline method, kernel regression method, and penalized spline regression method. The smoothing parameter is controlled the fitting model and the trade of between the bias of the estimator. We also propose the range of smoothing parameter of these methods to fit the smoothing function which data is nonlinear. Therefore, we mention the characteristic of smoothing function when the smoothing parameters have the various values. According to the results, it is concluded that the smoothing parameter of the smoothing spline method is suitable worked between zero to one, the kernel regression is good performance between two to ten, and the penalized spline is useful between one to ten. Key Words : Smoothing Parameter; Smoothing Technique; Smoothing Spline; Kernel Regression; Penalized Spline Regression Introduction The analysis of available explanatory variables has an application in regression function. The parametric and nonparametric method are the choices for estimating regression function between two variables that consisted of predictor variables and a response variable. A parametric regression model requires an assumption that the form of the underlying regression function such as linearity, stationary variance, and independence of explanatory variables. The selection of parametric model depends much on the problem and may be too restrictive in some applications. If an inappropriate

Silpakorn U Science & Tech J 6 (1) : 14-22, 2012

parametric model is used, it is possible to produce misleading conclusions. In other situation, a parametric model may not be available to use. To overcome the difficulty caused by the restrictive assumption of the parametric form of the regression function, one may remove the restriction that the regression function belongs to a parametric family. This approach leads to so-called nonparametric regression. Typically, the nonparametric regression methods are based on a smoothing technique which produces a smoother. A smoother is a tool for summarizing the trend of a response variable as

A. Araveeporn

Silpakorn U Science & Tech J Vol.6(1), 2012

Smoothing Techniques The nonparametric regression can be applied the smoothing techniques to fit the nonparametric regression function by using smoothing spline method, kernel regression method, and penalized spline regression method.

a function of one or more predictor variables. The single predictor case is called scatterplot smoothing that can be used to enhance the visual appearance of the scatterplot of response versus predictor variable, to help our eyes pick out the trend in the plot (Hastie and Tibshirani,1990). There are many smoothing techniques, e.g., a smoothing spline (Wahba, 1990, Green and Silverman, 1994), a kernel regression (Wand and Jones, 1995, Fan and Gijbels, 1996) , and a penalized spline regression (Ruppert, et al., 2003). The aim of smoothing techniques is to estimate smoothing estimators or smoothers that controlled by smoothing parameter. There are many methods that can be used to estimate the smoothing parameter. However, different methods of smoothing techniques have different methods of smoothing parameter, if we know the range of smoothing parameter that can be helped user for nonparametric regression analysis. In this article, we consider the nonparametric regression in Section 2 and apply in smoothing technique methods as a smoothing spline method, a kernel regression, and penalized spline regression in Section 3. In the Section 4, we show the variation of smoothing parameter in example data and conclude in Section 5.

The Smoothing Spline Method

Wahba (1990) defined the natural polynomial

spline s ( x) = snm ( x) is a real-valued function on [a, b] with the aid of n so-called knots ;

−∞ ≤ a < x1 < ... < xn < b < ∞ . The class of m -order spline with domain [a, b] will be denoted by W m [a, b] .

The natural measure associated with the

function

f ∈ W m [a, b] that used to measure the

roughness of curve which is called the quadratic penalty function given by b

∫{ f

(m)

( x)} dx 2

Consider the simple nonparametric regression model where the observation yt at design points xt , t = 1, 2,..., n assumed to satisfy

yt = f ( xt ) + ε t

, t = 1, 2,..., n

(3)

sn( m ) ( f ) = ∑ { yt − f ( xt )} + l ∫ { f ( m ) ( x)} dx (4)

(1)

t =1

where l > 0 denotes a smoothing parameter to be

where xt , t = 1, 2,..., n are known the predictor at

determined by a suitable cross-validation criteria

the time points, yt , t = 1, 2,..., n are the responses at the time points,

, t = 1, 2,..., n

where f (.) denotes a smooth function. To estimate fˆl (.) minimizes sn( m ) ( f ) over the class of function f (.) following

The Nonparametric Regression The simple nonparametric regression functions written as

yt = f ( xt ) + ε t

(2)

or information criteria. The smoothing parameter

f ( xt ) are the nonparametric

controls the trade-off between fidelity to the data and roughness of function, if l → ∞ , the fˆl (.)

regression function that we want to estimate, and

converges to linear function, if l → 0 , the fˆl (.)

ε t , t = 1, 2,..., n denote the measurement errors.

converges to interpolating spline.

Silpakorn U Science & Tech J Vol.6(1), 2012

The Estimation of Smoothing Parameter

In practice, this step can be implemented by using the function “smooth.spline” in the R software. Kernel Smoothing Nadaraya (1964) and Watson (1964) suggested the decomposition in estimating smoothing function for nonparametric regression . The smoothing estimator is written as

In this study, we emphasize m = 2

so-called the natural cubic spline which is commonly considered in the statistical literature (see Green and Silverman, 1994). We use this class of cubic smoothing spline to fit fˆl (.) by starting with the simple nonparametric regression model.

The first procedure of smoothing spline is

considered a least square problem to fit a function

 xt − x  y l  t ˆf ( x) = t =1 n x −x K t ∑   l  t =1 n

fˆl (.) that minimizes the residuals sum of squares n

RSS = ∑ { yt − f ( xt )}

∑ K 

(5)

t =1

Assuming the range f (.) in (3) is finite

= ∑ wt yt

interval, [a, b] = [ x(1) , x( n ) ] , where x(1) denotes

t =1

the i th order statistic and the roughness penalty

where l is known as the bandwidth parameter or called the smoothing parameter which is controlled the smoothness of the estimated curve and the kernel weights are given by,

of f (.) is measured by b

∫ { f ′′( x)}

(6)

This leads to the following penalized least squares regression to find

 xt − x  l  wt = nt =1 x −x K t ∑   l  t =1 n

∑ 

fˆl ( xt ) called the smoothing

spline estimator by minimizing

fˆl ( xt ) = arg min Sl ( f )

(7)

(9)

The smoothing parameter can be chosen using a

and b n 2 2 Sl ( f ) = ∑ { yt − f ( xt )} + l ∫ { f ′′( x)} dx (8)

cross-validation criteria. The kernel functions

where l > 0 is a smoothing parameter controlling

(triweight). Some popular kernel functions are

the size of the roughness penalty and used to trade-

shown in the Table 1.

t =1

K can be chosen to several kernel functions that are commonly used : Gaussian, uniform, triangle, Epanechnikov, quartic (biweight), and tricube

off the goodness of fit.

A. Araveeporn

Silpakorn U Science & Tech J Vol.6(1), 2012

Table 1 The kernel density functions Kernel

Kernel Density Function

K (u ) = (2π ) −1/ 2 e − u

Gaussian

, u ∈ [−∞, ∞]

Uniform

1 K (u ) = , u ∈ [−1,1] 2

Triangular

K (u ) = 1 − u , u ∈ [−1,1]

Epanechnikov

3 K (u ) = (1 − u 2 ), u ∈ [−1,1] 2

Quartic

K (u ) =

15 (1 − u 2 ) 2 , u ∈ [−1,1] 16

Tricube

K (u ) =

35 (1 − u 2 )3 , u ∈ [−1,1] 32

interior knots. A regression spline can be constructed using the k -th degree truncated power basis with K knots

The selection of the kernel function is not critical for the performance of regression function. However, it will be used the simplified Gaussian kernel that the smoothing estimator can be written in Gaussian density function by

τ 1 ,τ 2 ,...,τ K :

1, x,..., x k , ( x − τ 1 ) +k ,..., ( x − τ K ) +k (12)

1 1 x −x exp −  t ∑  yt π l 2 2   1 = t (10) fˆl ( x) = 2 n 1 1  xt − x  exp −  ∑  2 l  t =1 2π n

where w+k denotes k -th power of the positive part of w or written as w+k = {max(0, w)}k . The first

(k + 1) basis functions of the truncated power basis (12) are polynomials of degree up to k , and the

In this case, it is used the “ksmooth” function in the R software perform kernel regression estimator.

Penalized Spline Regression

Eubank(1988, 1999) introduced the regression

others are all the truncated power functions of degree

k . Conventionally, the truncated power basis of degree “k= 0,1,2, and 3” is denoted “constant, linear, quadratic” and “cubic” truncated power basis, respectively.

spline that the local neighborhoods are specified by

Using the truncated power basis in (12), a

a group of locations:

τ 0. ,τ 1 ,τ 2 ,...,τ K ,τ K +1

regression spline can be expressed as

(11)

s =0

r =1

interval [a, b] , where

f ( x) = ∑ β s x s + ∑ β k + r ( x − τ r ) k+ (13)

a = τ 0 < τ 1 < .... < τ K < τ K +1 = b . These locations are known as knots, and τ r , r = 1, 2,..., K are called

where β 0 , β1 ,..., β k + K are the unknown coefficients

in the range of

Silpakorn U Science & Tech J Vol.6(1), 2012

The Estimation of Smoothing Parameter

to be estimated by a suitable loss minization. The penalized spline is a method to estimate an unknown smooth function using the truncated power function (Ruppert and Carroll (2000)), and the penalized spline can be expressed as m −1

j =0

k =1

f ( xt ) = ∑ a j xtj + ∑ β k xt − τ k

2 m −1

The penalized spline smoothers is estimated by using the “SemiPar” function in the R software. The Example of Data Analysis In this section, the data are obtained from “Semiparametric Regression” (Ruppert et al, 2003). The data frame has 221 observations from a light detection and ranging (LIDAR) experiment which contains the range distance travelled before the light is reflected back to its source and logratio logarithm of the ratio of received light from two laser sources. Let yt denote the logratio logarithm of the range distance travelled with t where t = 390,..., 720 shown the scatterplot of LIDAR data in Figure 1

(14)

where a = [a 0 ,..., a m −1 ]T is the vector of the coefficients under the truncated power function,

β = [ β1 ,..., β K ]T ~ N (0, σ β2 Ω −1 / 2 (Ω1 / 2 ) Τ ) , and is τ l − τ k

the (l,k)th entry of Ω the coefficient of xt − τ k

2 m −1

and only

are penalized so that

a reasonably large order K can be used.

In this case, we focus on m=2, or the

so-called low-rank thin-plate spline which tends to have very good numerical properties. The low-rank thin-plate spline representation of f (.) is K

f ( xt , θ ) = a 0 + a1 xt + ∑ β k xt − τ k (15) 3

k =1

where θ = (a 0 , a 1 , β 1 ,..., β K ) T is the vector of regression coefficients, and τ 1 < τ 2 < ... < τ K are

fixed knots. The number of knots, K can be selected using a cross validation method or information theoretic methods (e.g., BIC or AIC). This class of penalized spline smoothers ,

Figure 1 The scatterplot of LIDAR data

fˆl (.) , may also be expressed in convenient vector form

fˆl = C (C T C + l 3 D) −1 C T y

From Figure 2-4 show the choice of smoothing parameter that profound influence on the fit using smoothing spline method, kernel regression method, and penalized spline regression method. When smoothing parameter is changed, the fitting lines have an effect on quality of the smoothing. If the smoothing parameter is too small, the fitting line interpolates between observed data. If the smoothing parameter is so large, the fitting line converges to linear function.

(16)

where

C = 1 

0 D =  2×2  0 K ×2

xt − τ k 1≤ k ≤ K  , 1≤t ≤ n 3

  (Ω ) Ω  2× K 1/ 2 T K

1/ 2 K

A. Araveeporn

Silpakorn U Science & Tech J Vol.6(1), 2012

Figure 2 The scatterplot of LIDAR data from smoothing spline method (smoothing parameter or l = 0.1, 0.5, 0.75, and 0.99)

Silpakorn U Science & Tech J Vol.6(1), 2012

The Estimation of Smoothing Parameter

Figure 3 The scatterplot of LIDAR data from kernel regression method (smoothing parameter or l = 2, 5, 10, and 100)

A. Araveeporn

Silpakorn U Science & Tech J Vol.6(1), 2012

Figure 4 The scatterplot of LIDAR data from penalized spline regression method (smoothing parameter or l = 1, 10, 100, and 1000)

The performance of the smoothing techniques is related about how close are the estimated values and the observed values. The Mean Square Error (MSE) is the criterion that are used to compare the performances of smoothing spline method, kernel regression, and penalized spline regression. This

criterion is defined as follows:

1 n MSE = ∑ ( yt − yˆt ) 2 n t =1 The MSE of these methods are given in Table 2.

Silpakorn U Science & Tech J Vol.6(1), 2012

The Estimation of Smoothing Parameter

Table 2 The MSE values and the smoothing parameter (l) of the smoothing techniques Smoothing spline

l = 0.1 l = 0.5 l = 0.75 l = 0.99

0.0037 0.0055 0.0059 0.0073

Kernel regression

l=2 l=5 l = 10 l = 100

0.0016 0.0050 0.0054 0.0070

Penalized spline

l=1 l = 10 l = 100 l = 1000

0.0053 0.0057 0.0062 0.0109

References Eubank, R. L. (1988) Spline Smoothing and Nonparametric Regression. Marcel Dekker, New York. Eubank, R. L. (1999) Nonparametric Regression and Spline Smoothing. Marcel Dekker, New York. Green, P. J. and Silverman, B. W. (1994) Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach. Chapman and Hall, London. Fan, J. and Gijbels, I. (1996) Local polynomial modeling and its applications. Chapman and Hall, London. Hastie, T. J. and Tibshirani, R. (1990) Generalized Additive Models. Chapman and Hall, London. Nadaraya, E. A. (1964) On estimating regression. Theory of Probability and Its Application, 9, 141-142. Ruppert, D. and Carroll, R. J. (2000) Spatialadaptive penalties for spline fitting. Australian and New Zealand Journal of Statistics, 42, 205-224. Ruppert, D., Wand, M. P., and Carroll. R. J. (2003) Semiparametric Regression. Cambridge University Press. Wahba, G. (1990) Spline Models for Observational Data. , SIAM, Philadelphia, PA. Wand, M. P. and Jones, M. C. (1995) Kernel Smoothing. Chapman and Hall, London. Watson, G.S. (1964) Smooth regression analysis. Sankhya, Series A, 26, 359-372.

From the Table 2, it is appeared out that Mean Square Error (MSE) of smoothing spline method, kernel regression method, and penalized spline regression method is slightly different where the smoothing parameters have been changed. The smoothing parameter of smoothing spline performs significantly between zero to one ( 0 < l < 1 ). The MSE of the kernel regression method is smaller than the MSEs of the other methods especially when smoothing parameter is more than one ( l > 1 ) but it should not be more than 10. The panelized spline regression method provides the slightly different in all smoothing parameter except when the smoothing parameter is so large. However, there are no criterion to define the value of smoothing parameter. The range of smoothing parameter can be considered for estimating smoothers. Conclusion We have been discussed the nonparametric regression based on the smoothing spline, kernel regression, and penalized spline regression that controlled by smoothing parameter. It is concluded that the smoothing parameter is different depended on the process of these methods. Therefore the estimation of the range of smoothing parameter has indicated a good performance by considering the MSE when the function in R program is worked reasonably when setup the values of smoothing parameter.

Research Article Confidence Intervals for the Parameter of a Gaussian First-Order Autoregressive Model with Additive Outliers: A Simulation Study Wararit Panichkitkosolkul 1*, Luckhana Saothayanun 2, Yupin Kanjanasakda 2 and Sunee Taweesakulvatchara 2 Department of Mathematics and Statistics, Faculty of Science and Technology,

Thammasat University, Phathumthani, Thailand Department of Applied Statistics, Faculty of Science, University of the Thai Chamber of Commerce,

Dindaeng, Bangkok, Thailand Corresponding author: E-mail: wararit@mathstat.sci.tu.ac.th

Received July 26, 2011; Accepted October 5, 2011 Abstract This paper is concerned with interval estimation of a parameter for a Gaussian first-order autoregressive model, AR(1), when there are additive outliers in a time series. We compared the confidence intervals based on the weighted symmetric estimator ( φˆ ), the recursive mean adjusted weighted symmetric estimator ( φˆ ), W

the recursive median adjusted weighted symmetric estimator ( φˆRDW ), and the improved recursive median adjusted weighted symmetric estimator ( φˆ ) by using Monte Carlo simulation. Simulation results have IRDW

shown that the confidence interval based on the estimator φˆIRDW is better than the other confidence intervals with respect to the coverage probability and the length criteria. Key Words: AR(1) model; Additive outliers; Confidence interval; Coverage probability; Length Introduction

corresponds to the situation in which a gross error

In time series analysis, outliers or atypical

of observation or recording error affects a single

observations can have adverse impacts on model

observation (Fox, 1972). An innovational outlier

identification, parameter estimation as well as

affects not only the particular observation but also

forecasting. Outliers may occur because of human

subsequent observations (Fox, 1972). In this study,

errors, such as typing, recording and measuring

we concentrate on the additive outliers because these

mistakes or because of abrupt, short-term changes in

outliers are more harmful than innovational outliers

the underlying process (Cryer and Chan, 2008). Fox

(Chatfield, 2001). A time series that does not contain

(1972), Abraham and Box (1979), and Martin (1980)

any outliers is called an outlier-free series.

discussed two kinds of outliers that can be founded

in time series data, namely, additive outliers (AO)

{ X t ; t = 2,3,..., n}

and innovational outliers (IO). An additive outlier

autoregressive model, AR(1), satisfying

Silpakorn U Science & Tech J 6 (1) : 23-41, 2012

Suppose an outlier-free time series follows a Gaussian first-order

Silpakorn U Science & Tech J Vol.6(1), 2012

Confidence Intervals for the Parameter of a Gaussian First-Order

X t = µ + φ ( X t −1 − µ ) + ε t ,

presented by Denby and Martin (1979). Guo (2000)

(1)

developed the simple and robust estimator for an

where µ is the mean of the model, φ is an

AR(1) model. Apart from that, So and Shin (1999)

autoregressive parameter; −1 < φ < 1, ε t ’s are

applied a recursive mean adjustment to the OLS

independent and identically distributed (i.i.d.)

estimator (ROLS) and they found that the mean

random variables having normal distribution with

square error of the ROLS estimator is smaller than

zero mean and variance σ ε2 , i.e., ε t ~ N (0,σ ε2 ). The

the OLS estimator for φ ∈ (0,1) . They also showed that the ROLS estimator has a coverage probability

model (1) will be called a random walk model if

which is close to the nominal value. Niwitpong

φ = 1, otherwise it is called a stationary model. In

(2007) applied the recursive mean adjustment to

the case of φ close to one or near a non-stationary

the weighted symmetric estimator (RW) of Park and

model, the mean and variance of this model change

Fuller (1995). Panichkitkosolkul (2010a) proposed

over time. Let the observed time series be denoted

an estimator for an unknown mean Gaussian

by {Yt } . An additive outlier model is defined as

Yt = X t + ω I t(T ) ,

AR(1) model with additive outliers by applying the recursive median adjustment to the weighted

(2)

symmetric estimator (RDW). He found that the

where ω is the magnitude of the additive outliers

RDW estimator provides the efficiency more than

and I t(T ) is the indicator function such that

the W and RW estimators in terms of the mean

 1 , t = T, I t(T ) =   0 , t ≠ T. The model (2) can be interpreted that { X t } has

square error for almost all situations. Moreover, Panichkitkosolkul (2010b) also improved the RDW estimator by applying the new recursive median adjustment to the weighted symmetric estimator

additive outliers at time point T (1 < T < n).

(IRDW). New recursive median adjustment can

One of the well-known estimators of an

be derived from computing the double recursive

autoregressive parameter; φ is the ordinary least

median. Using the simulations, an IRDW estimator

squares (OLS) estimator. Although the OLS

performs better than the W, RW and RDW estimators

estimator has asymptotic normality for φ < 1 (see,

in terms of the mean square error for almost all

Mann and Wald, 1943; Brockwell and Davis, 1991),

scenarios. Thus, our major purpose in this paper is

it has long been known that the OLS estimator can

to evaluate the efficiency of the confidence intervals

have large bias; see, for example, Marriott and Pope

for the parameter of a Gaussian AR(1) model based

(1954), Shaman and Stine (1988), Newbold and

on the W, RW, RDW and IRDW estimators when

Agiakloglou (1993). In addition, Conover (1980)

there are additive outliers in a time series data.

indicated that the OLS estimator is sensitive to

outliers (see Conover, 1980, pp.267). Therefore,

The rest of this paper is structured as follows.

In the following section, we describe the confidence

there have been the useful improvements in the

intervals of the parameter of a Gaussian AR(1) model

parameter estimation so as to reduce the bias of the

based on the W, RW, RDW and IRDW estimators.

OLS estimator. Park and Fuller (1995) proposed

Simulation results obtained from Monte Carlo

the weighted symmetric estimator (W) of φ . The

simulation are shown in the third section. In the

robust estimator for an autoregressive model was

forth section, all confidence intervals are illustrated

W. Panichkitkosolkul et.al

Silpakorn U Science & Tech J Vol.6(1), 2012

Based on φˆRW , the (1 − a )100% confidence interval

and compared through empirical application. The discussions of the results and conclusions are

for φ of model (1) is defined as

presented in the final section.

  CI RW = φˆRW − Z a SE (φˆRW ) ,φˆRW + Z a SE (φˆRW )  , (6) 1− 1− 2 2  

Methodology Park and Fuller (1995) proposed the weighted

σˆ RW

SE (φˆRW ) =

where

symmetric estimator of φ for model (1) given by

∑ (Y

∑ (Yt − Y )(Yt −1 − Y )

φˆW =

t =2

∑ (Yt −1 − Y ) + n 2

−1

t =3

∑ (Yt − Y )

(3) 2 σˆ RW =

t =1

1−

as follows

σˆW

∑ (Y

t −1

t =2

∑ ( (Y − Y ) − φˆ n

σˆW2 = t = 2

n−2

It is well known that if there are outliers in

The estimator of φ based on the recursive median

and Z

1−

adjustment called the RDW estimator is given by

φˆ

RDW

1 ∑ Yi in (3). The estimator of φ t i =1

∑ (Y t =3

t −1

CI RDW

t −1

−1

− Yt −1 ) + n

− Yt −1 ) n

∑ (Y − Y ) t =1

t −1

− Yt −1 ) n

∑ (Yt −1 − Yt −1 )2 + n−1 ∑ (Yt − Yt )2

(7)

t =1

confidence interval for φ of model (1) based on φˆRDW is

obtained as a result of this recursive mean adjustment is

t =2

 where Yt = median(Y1 , Y2 ,..., Yt ). The (1 − a )100%

∑ (Y − Y )(Y

∑ (Y − Y )(Y t =3

adjustment to the weighted symmetric estimator. He

φˆ

and

n−2

recursive mean Yt in (5) by the recursive median.

So and Shin (1999) by applying the recursive mean

(2010a) improved the RW estimator by replacing the

Niwitpong (2007) extended the concepts of

replaces Y by Yt =

)

outliers than the mean. Therefore, Panichkitkosolkul

 a a 1 −  th quantile of the standard normal 2  distribution.

(Yt −1 − Yt −1 )

On the other hand, the median is less sensitive to

− Y )2

)

the data set then the mean will be strongly affected.

(Yt −1 − Y )

t =2

  CIW = φˆW − Z a SE (φˆW ) ,φˆW + Z a SE (φˆW )  , (4) 1− 1− 2 2   n

− Yt −1 )

 a is a 1 −  th quantile of the standard normal 2  2 distribution.

SE (φˆW ) =

∑ ( (Y − Y ) − φˆ n

Therefore, the (1 − a )100% confidence interval for φ of model (1) based on φˆ can be derived

where

t −1

t =2

, 2

(5) 2

where

φˆRDW − Z a SE (φˆRDW ) ,  1−   2 =  , (8) φˆRDW + Z a SE (φˆRDW )   1− 2  

SE (φˆRDW ) =

σˆ RDW n

∑ (Yt −1 − Yt −1 )2 t =2

Silpakorn U Science & Tech J Vol.6(1), 2012

∑ ( (Y − Y ) − φˆ n

2 σˆ RDW =

1−

a 2

t =2

RDW

Confidence Intervals for the Parameter of a Gaussian First-Order

(Yt −1 − Yt −1 )

)

2 σˆ IRDW =

and

n−2

t =2

IRDW

 (Yt −1 − Yt −1 )

)

n−2

and

 a is a 1 −  th quantile of the standard normal 2  2 distribution.

 a is a 1 −  th quantile of the standard normal 2 

1−

distribution.

∑ ( (Y − Y ) − φˆ n

Further, Panichkitkosolkul (2010b) also

To study the different confidence intervals,

we consider their coverage probability and length.

reduced the effect of outliers on an estimator of φ

For each of the methods considered, we obtain a

in model (1) by using the new recursive median

(1 − a )100% confidence interval denoted by ( L,U )

adjustment. The new recursive median values

(based on M = 5,000 replicates) and estimated the

are derived from computing the double recursive

coverage probability and the length, respectively, by

median. There are two steps for computing the new recursive median. Firstly, the recursive median ( Y )

#( L ≤ φ ≤ U ) 1 −a = , M

are computed by using observed time series data Yt . Secondly, we calculate the double recursive median

by using the recursive median obtained from the

 = Length

and

first step. Therefore, the recursive median in (7) is replaced by the improved recursive median. This

∑ (U i =1

− Li )

estimator is abbreviated the IRDW estimator. The

where #( L ≤ φ ≤ U ) denotes the number of

estimator of φ improved by using the improved

simulations for which an autoregressive parameter;

recursive median is defined as

φ lies within the confidence interval ( L,U ).

φˆIRDW =

∑ (Y − Y )(Y n

t =2

∑ (Yt −1 − Yt −1 )2 + n−1 ∑ (Yt − Yt )2 t =3

where

− Yt −1 )

t −1

(9)

is presented in order to evaluate the performance of the confidence intervals CIW , CI RW , CI RDW and

t =1

Yt = median(Y1 , Y2 ,..., Yt )

In the following section, the simulation results

CI IRDW based on their coverage probabilities and and

lengths.

Yt = median(Y1 , Y2 ,..., Yt ). An R function for computing the estimator in (9) is given in the

Simulation Results

Appendix of Panichkitkosolkul (2010b). In addition,

the (1 − a )100% confidence interval for φ of model

performance of the confidence intervals (4), (6), (8) and (10) via simulations. The data sets of five-

(1) based on the IRDW estimator is

CI IRDW

where

thousand Gaussian AR(1) time series with AOs

φÎRDW − Z a SE (φÎRDW ) ,  1−   2 =  , (10) φÎRDW + Z a SE (φÎRDW )   1−   2

SE (φˆIRDW ) =

σˆ IRDW n

∑ (Yt −1 − Yt −1 )2

This section is devoted to access the

were simulated by using R statistical software (The R Development Core Team, 2010a, 2010b). The scope of the simulations is set under ( µ ,σ ε ) = (0, 1); φ = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8

t =2

W. Panichkitkosolkul et.al

Silpakorn U Science & Tech J Vol.6(1), 2012

and 0.9; sample sizes n = 25, 50, 100 and 250; the

the CI IRDW provides the coverage probabilities

magnitudes of the AOs ω = 0, 3σ ε , 5σ ε , − 3σ ε and

larger than those of other confidence intervals.

−5σ ε ; the percentages of additive outliers p = 5%

For moderate sample size (n = 50) , the coverage

and 10% . The confidence level is fixed at 0.05.

probability of the CI RDW is the largest compared

Additionally, the additive outliers arose randomly.

to other confidence intervals when the parameter

Our simulation results are summarized in Tables 1-9.

is small (φ = 0.1 and 0.2). In case of 0.3 ≤ φ ≤ 0.9,

Table 1 show the results on coverage probabilities

the CI IRDW provides the coverage probabilities

and lengths of prediction intervals when there are

larger than those of other confidence intervals. For

no outliers in time series (ω = 0). Tables 2-5 present

large sample sizes (n = 100 and 250), the coverage

the simulation results for p = 5%. Similarly, Tables

probability of the CI IRDW is the largest compared to

6-9 present the results for p = 10% .

other confidence intervals except when φ = 0.1 and

n = 100.

We begin with the results in the case when

there are no outliers (ω = 0) shown in Table 1. For

The results in case of ω = 5σ ε and −5σ ε at

small sample size (n = 25), the coverage probability

p = 5% are shown in Tables 4 and 5. For small

of the CI RDW is the largest compared to other

and moderate sample sizes (n = 25, 50 and 100),

confidence intervals when the parameter is small

the coverage probability of the CI IRDW is the largest

(0.1 ≤ φ ≤ 0.5). When φ = 0.6 and 0.7, the CI RW

compared to other confidence intervals except

provides the coverage probabilities larger than those

when φ = 0.1. For large sample size (n = 250), the

of other confidence intervals. The CI IRDW , on the

coverage probability of the CI IRDW is the largest

other hand, provides the coverage probabilities

compared to other confidence intervals.

close to the nominal confidence level (0.95) when

the parameter is close to one (φ = 0.8 and 0.9).

and −3σ ε at p = 10% are reported. For small sample

For moderate sample sizes (n = 50 and 100), the

size (n = 25), the coverage probability of the CI IRDW

coverage probability of the CI RW is the largest

is the largest compared to other confidence intervals

compared to other confidence intervals for almost

when the parameter is small (φ = 0.1 and 0.2). In

all φ values except when φ = 0.9. For large sample

case of 0.3 ≤ φ ≤ 0.9 , the CI IRDW provides the

size (n = 250), the CI RW provides the coverage

coverage probabilities larger than those of other

probabilities close to the nominal confidence level

confidence intervals. For moderate sample sizes

for all cases.

(n = 50 and 100), the coverage probability of the

In Tables 6 and 7, the results in case of ω = 3σ ε

The results in case of ω = 3σ ε and −3σ ε at

CI IRDW is the largest compared to other confidence

p = 5% are reported in Tables 2 and 3, respectively.

intervals except when φ = 0.1. For large sample size

For small sample size (n = 25), the coverage

(n = 250), the coverage probability of the CI IRDW is

probability of the CI RDW is the largest compared

the largest compared to other confidence intervals

to other confidence intervals when the parameter is

for all autoregressive parameter values considered.

small ( φ = 0.1, 0.2 and 0.3). In case of 0.4 ≤ φ ≤ 0.9,

Silpakorn U Science & Tech J Vol.6(1), 2012

Confidence Intervals for the Parameter of a Gaussian First-Order

The results in case of ω = 5σ ε and −5σ ε

get larger. This is intuitive in nature because as n

at p = 10% are shown in Tables 8 and 9. They

increases it is possible to estimate the standard error

are similar to Tables 6 and 7 so that we omit the

of the estimator more accurately. Consequently, the

explanation in the details.

length decreases when the sample increases.

Furthermore, the CI IRDW dominates the

Apart from that, if the magnitude of the AOs

other confidence intervals with respect to the

increases, then the coverage probability decreases

length criterion. Namely, the lengths of the CI IRDW

(compare between Table 2 and Table 4) while

are shortest with comparing those of any other

the length increases. Similarly, if the percentage

confidence intervals except when n = 25 and

of additive outliers increases, then the coverage

φ = 0.1 of Tables 2, 4, 5, 8 and 9. Additionally,

probability decreases (compare between Table 2

the coverage probabilities decrease as sample sizes

and Table 6) while the length increases.

W. Panichkitkosolkul et.al

Silpakorn U Science & Tech J Vol.6(1), 2012

Table 1 The estimated coverage probabilities and lengths of confidence intervals CIW , CI RW , CI RDW and

CI IRDW when no outliers (Ď&#x2030; = 0).

Ď&#x2020;

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

100

250

W 0.9410 0.9382 0.9360 0.9350 0.9276 0.9248 0.9090 0.8918 0.8650 0.9410 0.9516 0.9438 0.9414 0.9422 0.9422 0.9340 0.9226 0.9042 0.9500 0.9478 0.9376 0.9508 0.9434 0.9422 0.9420 0.9320 0.9230 0.9496 0.9492 0.9510 0.9430 0.9484 0.9494 0.9528 0.9400 0.9380

Coverage probabilities RW RDW 0.9530 0.9566 0.9558 0.9564 0.9524 0.9568 0.9520 0.9542 0.9486 0.9504 0.9484 0.9482 0.9368 0.9346 0.9236 0.9162 0.8886 0.8906 0.9490 0.9446 0.9568 0.9560 0.9536 0.9512 0.9478 0.9468 0.9516 0.9550 0.9520 0.9488 0.9448 0.9428 0.9332 0.9298 0.9104 0.9100 0.9520 0.9464 0.9512 0.9518 0.9434 0.9430 0.9540 0.9532 0.9480 0.9476 0.9478 0.9452 0.9454 0.9426 0.9382 0.9324 0.9252 0.9260 0.9514 0.9506 0.9502 0.9486 0.9520 0.9494 0.9470 0.9460 0.9486 0.9466 0.9510 0.9496 0.9544 0.9518 0.9418 0.9380 0.9388 0.9372

IRDW 0.9048 0.9026 0.9090 0.9166 0.9224 0.9288 0.9362 0.9426 0.9376 0.8822 0.8914 0.8930 0.8962 0.8982 0.9012 0.9170 0.9234 0.9432 0.8810 0.8930 0.8836 0.8950 0.8838 0.8948 0.8892 0.9008 0.9200 0.9010 0.9036 0.9000 0.8888 0.8930 0.8988 0.8938 0.8812 0.8970

W 0.8016 0.7944 0.7808 0.7600 0.7337 0.6972 0.6560 0.5989 0.5360 0.5586 0.5524 0.5405 0.5227 0.4994 0.4682 0.4287 0.3787 0.3157 0.3924 0.3873 0.3781 0.3646 0.3463 0.3227 0.2919 0.2522 0.1971 0.2473 0.2437 0.2376 0.2284 0.2164 0.2007 0.1799 0.1529 0.1149

Lengths RW RDW 0.8181 0.8164 0.8086 0.8058 0.7914 0.7875 0.7672 0.7640 0.7378 0.7348 0.6980 0.6963 0.6533 0.6523 0.5931 0.5937 0.5265 0.5276 0.5639 0.5627 0.5565 0.5548 0.5434 0.5412 0.5242 0.5222 0.4998 0.4976 0.4673 0.4653 0.4262 0.4242 0.3751 0.3733 0.3110 0.3099 0.3941 0.3936 0.3884 0.3875 0.3790 0.3779 0.3651 0.3639 0.3463 0.3450 0.3221 0.3209 0.2909 0.2896 0.2507 0.2493 0.1952 0.1938 0.2477 0.2475 0.2440 0.2437 0.2378 0.2374 0.2285 0.2281 0.2163 0.2159 0.2005 0.2000 0.1795 0.1790 0.1525 0.1519 0.1143 0.1137

IRDW 0.7995 0.7822 0.7572 0.7269 0.6901 0.6446 0.5960 0.5297 0.4592 0.5551 0.5435 0.5258 0.5026 0.4730 0.4363 0.3911 0.3359 0.2694 0.3905 0.3827 0.3709 0.3544 0.3329 0.3062 0.2721 0.2292 0.1714 0.2467 0.2421 0.2350 0.2247 0.2115 0.1946 0.1724 0.1438 0.1041

Silpakorn U Science & Tech J Vol.6(1), 2012

Confidence Intervals for the Parameter of a Gaussian First-Order

Table 2 The estimated coverage probabilities and lengths of confidence intervals CIW , CI RW , CI RDW and

CI IRDW when p = 5% and ω = 3σ ε .

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

100

250

W 0.9374 0.9238 0.9002 0.8690 0.8404 0.7982 0.7598 0.7178 0.6700 0.9336 0.9156 0.8872 0.8476 0.8096 0.7534 0.7314 0.6924 0.6620 0.9334 0.8904 0.8330 0.7542 0.6586 0.6010 0.5448 0.5258 0.5576 0.9186 0.8390 0.7000 0.5634 0.4154 0.3286 0.2612 0.2790 0.3856

Coverage probabilities RW RDW 0.9550 0.9640 0.9466 0.9500 0.9290 0.9358 0.9074 0.9164 0.8832 0.8954 0.8434 0.8546 0.8104 0.8128 0.7726 0.7654 0.7100 0.7070 0.9420 0.9486 0.9286 0.9370 0.9128 0.9188 0.8704 0.8814 0.8408 0.8444 0.7892 0.7986 0.7666 0.7708 0.7252 0.7268 0.6770 0.6834 0.9442 0.9512 0.9046 0.9180 0.8508 0.8702 0.7820 0.7982 0.6848 0.7036 0.6272 0.6434 0.5722 0.5876 0.5458 0.5596 0.5664 0.5754 0.9258 0.9392 0.8516 0.8714 0.7190 0.7508 0.5854 0.6126 0.4332 0.4660 0.3430 0.3634 0.2756 0.3012 0.2876 0.3100 0.3886 0.4068

IRDW 0.9298 0.9348 0.9342 0.9346 0.9246 0.9120 0.8960 0.8668 0.8324 0.9194 0.9250 0.9286 0.9072 0.9028 0.8884 0.8740 0.8508 0.8258 0.9310 0.9296 0.9072 0.8750 0.8172 0.7928 0.7510 0.7428 0.7616 0.9396 0.9088 0.8366 0.7498 0.6360 0.5596 0.5178 0.5392 0.6380

W 0.8024 0.7996 0.7927 0.7808 0.7646 0.7426 0.7127 0.6720 0.6161 0.5595 0.5561 0.5496 0.5397 0.5242 0.5045 0.4739 0.4340 0.3745 0.3934 0.3908 0.3860 0.3786 0.3687 0.3530 0.3314 0.2983 0.2462 0.2479 0.2461 0.2428 0.2377 0.2306 0.2199 0.2050 0.1819 0.1438

Lengths RW RDW 0.8150 0.8144 0.8108 0.8088 0.8016 0.7997 0.7884 0.7862 0.7697 0.7672 0.7454 0.7432 0.7133 0.7111 0.6705 0.6691 0.6119 0.6122 0.5635 0.5627 0.5594 0.5583 0.5523 0.5510 0.5416 0.5399 0.5253 0.5237 0.5046 0.5029 0.4729 0.4711 0.4317 0.4297 0.3712 0.3688 0.3946 0.3942 0.3918 0.3912 0.3868 0.3859 0.3790 0.3781 0.3689 0.3679 0.3528 0.3518 0.3308 0.3296 0.2973 0.2959 0.2447 0.2429 0.2482 0.2480 0.2463 0.2460 0.2430 0.2426 0.2378 0.2374 0.2306 0.2301 0.2198 0.2193 0.2048 0.2043 0.1815 0.1810 0.1434 0.1425

IRDW 0.8027 0.7923 0.7783 0.7581 0.7324 0.7011 0.6601 0.6095 0.5415 0.5577 0.5504 0.5400 0.5251 0.5041 0.4784 0.4409 0.3926 0.3252 0.3923 0.3880 0.3811 0.3715 0.3589 0.3399 0.3141 0.2758 0.2174 0.2475 0.2450 0.2410 0.2351 0.2269 0.2149 0.1983 0.1728 0.1317

W. Panichkitkosolkul et.al

Silpakorn U Science & Tech J Vol.6(1), 2012

Table 3 The estimated coverage probabilities and lengths of confidence intervals CIW , CI RW , CI RDW and

CI IRDW when p = 5% and ω = −3σ ε .

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

100

250

W 0.9406 0.9246 0.8964 0.8752 0.8428 0.8006 0.7572 0.7222 0.6832 0.9386 0.9216 0.8912 0.8524 0.8076 0.7576 0.7132 0.6880 0.6706 0.9368 0.8922 0.8308 0.7546 0.6662 0.5834 0.5274 0.5126 0.5524 0.9094 0.8250 0.7090 0.5564 0.4136 0.3256 0.2730 0.2854 0.3710

Coverage probabilities RW RDW 0.9544 0.9614 0.9456 0.9512 0.9322 0.9394 0.9118 0.9214 0.8896 0.8942 0.8516 0.8576 0.8082 0.8152 0.7702 0.7684 0.7234 0.7206 0.9490 0.9544 0.9386 0.9446 0.9132 0.9204 0.8802 0.8894 0.8364 0.8472 0.7944 0.8070 0.7504 0.7564 0.7184 0.7240 0.6886 0.6914 0.9434 0.9470 0.9066 0.9174 0.8534 0.8720 0.7818 0.8062 0.6924 0.7102 0.6140 0.6336 0.5528 0.5708 0.5320 0.5466 0.5588 0.5788 0.9164 0.9298 0.8392 0.8634 0.7238 0.7544 0.5778 0.6060 0.4308 0.4600 0.3394 0.3616 0.2858 0.3062 0.2946 0.3100 0.3732 0.3958

IRDW 0.9304 0.9454 0.9402 0.9354 0.9284 0.9098 0.8874 0.8668 0.8424 0.9248 0.9292 0.9276 0.9188 0.9066 0.8866 0.8598 0.8498 0.8336 0.9260 0.9288 0.9134 0.8780 0.8316 0.7860 0.7544 0.7364 0.7664 0.9348 0.9072 0.8422 0.7404 0.6312 0.5540 0.5172 0.5362 0.6314

W 0.8031 0.7998 0.7937 0.7821 0.7636 0.7428 0.7121 0.6703 0.6159 0.5598 0.5562 0.5496 0.5394 0.5250 0.5043 0.4755 0.4341 0.3741 0.3934 0.3908 0.3860 0.3789 0.3685 0.3537 0.3314 0.2990 0.2456 0.2479 0.2461 0.2428 0.2378 0.2306 0.2199 0.2047 0.1820 0.1444

Lengths RW RDW 0.8158 0.8149 0.8111 0.8093 0.8032 0.8011 0.7893 0.7874 0.7688 0.7663 0.7457 0.7432 0.7129 0.7112 0.6681 0.6664 0.6114 0.6115 0.5637 0.5630 0.5593 0.5582 0.5522 0.5507 0.5413 0.5397 0.5260 0.5241 0.5043 0.5026 0.4745 0.4726 0.4320 0.4297 0.3707 0.3687 0.3946 0.3942 0.3919 0.3912 0.3868 0.3859 0.3794 0.3784 0.3687 0.3677 0.3537 0.3526 0.3309 0.3296 0.2980 0.2966 0.2440 0.2421 0.2482 0.2480 0.2463 0.2461 0.2430 0.2426 0.2379 0.2375 0.2306 0.2302 0.2199 0.2194 0.2045 0.2039 0.1817 0.1811 0.1439 0.1431

IRDW 0.8029 0.7935 0.7794 0.7596 0.7310 0.7021 0.6606 0.6070 0.5399 0.5581 0.5505 0.5398 0.5252 0.5050 0.4786 0.4420 0.3932 0.3251 0.3922 0.3880 0.3811 0.3718 0.3587 0.3408 0.3141 0.2765 0.2167 0.2475 0.2451 0.2410 0.2352 0.2270 0.2149 0.1979 0.1729 0.1322

Silpakorn U Science & Tech J Vol.6(1), 2012

Confidence Intervals for the Parameter of a Gaussian First-Order

Table 4 The estimated coverage probabilities and lengths of confidence intervals CIW , CI RW , CI RDW and

CI IRDW when p = 5% and ω = 5σ ε .

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

100

250

W 0.9484 0.9212 0.8552 0.7830 0.6950 0.6034 0.5238 0.4398 0.4108 0.9402 0.8784 0.7770 0.6664 0.5564 0.4378 0.3670 0.3292 0.3392 0.9072 0.7910 0.5776 0.3880 0.2248 0.1288 0.0928 0.0828 0.1346 0.8502 0.5756 0.2714 0.0924 0.0218 0.0048 0.0018 0.0028 0.0116

Coverage probabilities RW RDW 0.9618 0.9704 0.9474 0.9562 0.8940 0.9074 0.8404 0.8552 0.7580 0.7730 0.6668 0.6724 0.5942 0.5932 0.5060 0.5034 0.4630 0.4566 0.9502 0.9578 0.9028 0.9168 0.8156 0.8374 0.7026 0.7198 0.6018 0.6160 0.4800 0.4934 0.4126 0.4136 0.3584 0.3686 0.3570 0.3712 0.9174 0.9304 0.8156 0.8534 0.6090 0.6630 0.4186 0.4650 0.2454 0.2792 0.1468 0.1642 0.1058 0.1178 0.0910 0.1024 0.1418 0.1574 0.8624 0.9042 0.5946 0.6850 0.2894 0.3594 0.1032 0.1364 0.0240 0.0366 0.0056 0.0076 0.0020 0.0026 0.0030 0.0036 0.0122 0.0180

IRDW 0.9640 0.9624 0.9366 0.9128 0.8604 0.7940 0.7532 0.6892 0.6442 0.9554 0.9368 0.8902 0.8236 0.7534 0.6808 0.6112 0.5832 0.5798 0.9302 0.8958 0.7624 0.6092 0.4500 0.3364 0.2756 0.2774 0.3720 0.9190 0.7608 0.4838 0.2382 0.0910 0.0380 0.0258 0.0404 0.1150

W 0.8046 0.8036 0.8012 0.7966 0.7886 0.7763 0.7579 0.7308 0.6879 0.5610 0.5592 0.5559 0.5510 0.5423 0.5315 0.5129 0.4828 0.4337 0.3938 0.3928 0.3908 0.3875 0.3824 0.3744 0.3606 0.3380 0.2934 0.2482 0.2474 0.2459 0.2435 0.2398 0.2341 0.2245 0.2076 0.1739

Lengths RW RDW 0.8140 0.8138 0.8117 0.8112 0.8086 0.8079 0.8028 0.8016 0.7933 0.7925 0.7798 0.7793 0.7607 0.7594 0.7325 0.7312 0.6870 0.6864 0.5639 0.5633 0.5617 0.5609 0.5580 0.5570 0.5527 0.5516 0.5433 0.5420 0.5320 0.5308 0.5125 0.5111 0.4818 0.4799 0.4318 0.4293 0.3947 0.3942 0.3935 0.3929 0.3914 0.3906 0.3880 0.3870 0.3827 0.3816 0.3745 0.3734 0.3604 0.3592 0.3375 0.3361 0.2923 0.2902 0.2484 0.2482 0.2476 0.2473 0.2461 0.2456 0.2436 0.2431 0.2399 0.2392 0.2341 0.2334 0.2244 0.2237 0.2074 0.2067 0.1735 0.1726

IRDW 0.8071 0.8015 0.7955 0.7847 0.7698 0.7499 0.7193 0.6814 0.6234 0.5605 0.5564 0.5503 0.5425 0.5286 0.5134 0.4876 0.4472 0.3857 0.3932 0.3912 0.3879 0.3832 0.3761 0.3655 0.3474 0.3188 0.2647 0.2479 0.2467 0.2447 0.2417 0.2373 0.2305 0.2192 0.1996 0.1613

W. Panichkitkosolkul et.al

Silpakorn U Science & Tech J Vol.6(1), 2012

Table 5 The estimated coverage probabilities and lengths of confidence intervals CIW , CI RW , CI RDW and

CI IRDW when p = 5% and ω = −5σ ε .

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

100

250

W 0.9570 0.9130 0.8670 0.7862 0.6960 0.5898 0.5226 0.4398 0.4034 0.9382 0.8690 0.7916 0.6690 0.5486 0.4296 0.3598 0.3186 0.3288 0.9112 0.7838 0.5724 0.3890 0.2306 0.1342 0.0872 0.0834 0.1202 0.8540 0.5806 0.2586 0.0898 0.0258 0.0060 0.0034 0.0030 0.0138

Coverage probabilities RW RDW 0.9680 0.9738 0.9374 0.9506 0.9040 0.9098 0.8378 0.8458 0.7598 0.7618 0.6588 0.6648 0.5962 0.5986 0.5078 0.5018 0.4570 0.4516 0.9476 0.9540 0.8934 0.9100 0.8274 0.8444 0.7128 0.7322 0.5944 0.6114 0.4716 0.4854 0.3954 0.4076 0.3534 0.3690 0.3500 0.3616 0.9216 0.9350 0.8090 0.8440 0.6044 0.6604 0.4184 0.4626 0.2584 0.2844 0.1490 0.1712 0.0990 0.1120 0.0926 0.1018 0.1252 0.1424 0.8646 0.9080 0.5980 0.6864 0.2744 0.3464 0.0962 0.1294 0.0284 0.0376 0.0064 0.0116 0.0042 0.0042 0.0034 0.0044 0.0142 0.0208

IRDW 0.9622 0.9602 0.9414 0.9084 0.8586 0.7924 0.7422 0.6804 0.6400 0.9500 0.9328 0.8984 0.8276 0.7544 0.6644 0.6158 0.5770 0.5794 0.9350 0.8914 0.7546 0.6118 0.4516 0.3340 0.2610 0.2792 0.3528 0.9178 0.7636 0.4672 0.2270 0.0976 0.0432 0.0290 0.0348 0.1224

W 0.8053 0.8041 0.8013 0.7954 0.7885 0.7764 0.7568 0.7311 0.6882 0.5606 0.5590 0.5561 0.5509 0.5433 0.5320 0.5129 0.4833 0.4338 0.3938 0.3929 0.3909 0.3875 0.3823 0.3744 0.3613 0.3376 0.2943 0.2482 0.2474 0.2460 0.2436 0.2399 0.2340 0.2245 0.2078 0.1740

Lengths RW RDW 0.8142 0.8138 0.8122 0.8116 0.8083 0.8074 0.8015 0.8007 0.7937 0.7925 0.7805 0.7793 0.7587 0.7575 0.7321 0.7309 0.6874 0.6866 0.5634 0.5629 0.5615 0.5607 0.5582 0.5572 0.5525 0.5514 0.5444 0.5432 0.5327 0.5315 0.5127 0.5115 0.4824 0.4806 0.4318 0.4292 0.3947 0.3943 0.3937 0.3930 0.3916 0.3907 0.3879 0.3870 0.3826 0.3815 0.3745 0.3734 0.3611 0.3600 0.3370 0.3357 0.2932 0.2912 0.2484 0.2482 0.2476 0.2472 0.2462 0.2457 0.2437 0.2431 0.2399 0.2393 0.2340 0.2333 0.2244 0.2237 0.2076 0.2069 0.1736 0.1727

IRDW 0.8068 0.8017 0.7944 0.7834 0.7699 0.7504 0.7182 0.6819 0.6242 0.5601 0.5563 0.5506 0.5420 0.5305 0.5139 0.4877 0.4481 0.3859 0.3932 0.3913 0.3881 0.3832 0.3761 0.3652 0.3485 0.3185 0.2659 0.2478 0.2466 0.2448 0.2418 0.2374 0.2304 0.2192 0.1999 0.1611

Silpakorn U Science & Tech J Vol.6(1), 2012

Confidence Intervals for the Parameter of a Gaussian First-Order

Table 6 The estimated coverage probabilities and lengths of confidence intervals CIW , CI RW , CI RDW and

CI IRDW when p = 10% and ω = 3σ ε .

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

100

250

W 0.9354 0.9034 0.8670 0.8192 0.7506 0.6730 0.6134 0.5564 0.5172 0.9252 0.8860 0.7994 0.7060 0.5990 0.5122 0.4460 0.4084 0.3972 0.9174 0.8184 0.6950 0.5520 0.3974 0.2882 0.2340 0.2238 0.2770 0.8744 0.6870 0.4308 0.2088 0.0870 0.0366 0.0222 0.0208 0.0690

Coverage probabilities RW RDW 0.9508 0.9570 0.9288 0.9406 0.9074 0.9212 0.8622 0.8802 0.8120 0.8234 0.7372 0.7424 0.6812 0.6894 0.6216 0.6286 0.5710 0.5712 0.9396 0.9512 0.9080 0.9266 0.8294 0.8562 0.7476 0.7812 0.6480 0.6824 0.5610 0.5784 0.4880 0.5098 0.4414 0.4600 0.4196 0.4288 0.9292 0.9438 0.8410 0.8762 0.7226 0.7652 0.5812 0.6272 0.4288 0.4652 0.3154 0.3496 0.2546 0.2832 0.2396 0.2572 0.2852 0.3030 0.8830 0.9172 0.7032 0.7792 0.4514 0.5252 0.2230 0.2796 0.0958 0.1292 0.0404 0.0524 0.0236 0.0302 0.0224 0.0280 0.0696 0.0786

IRDW 0.9336 0.9342 0.9404 0.9168 0.8868 0.8442 0.8134 0.7722 0.7344 0.9296 0.9324 0.9060 0.8630 0.8036 0.7508 0.6856 0.6582 0.6320 0.9330 0.9108 0.8408 0.7584 0.6322 0.5452 0.4902 0.4758 0.5418 0.9270 0.8390 0.6490 0.4252 0.2538 0.1554 0.1186 0.1378 0.2706

W 0.8024 0.8001 0.7965 0.7892 0.7787 0.7618 0.7391 0.7081 0.6600 0.5600 0.5586 0.5545 0.5487 0.5405 0.5261 0.5061 0.4740 0.4225 0.3937 0.3922 0.3892 0.3843 0.3773 0.3662 0.3494 0.3226 0.2736 0.2481 0.2470 0.2449 0.2418 0.2368 0.2293 0.2178 0.1985 0.1625

Lengths RW RDW 0.8134 0.8118 0.8100 0.8081 0.8050 0.8029 0.7966 0.7942 0.7843 0.7820 0.7663 0.7636 0.7418 0.7387 0.7085 0.7060 0.6583 0.6557 0.5633 0.5621 0.5614 0.5598 0.5570 0.5551 0.5506 0.5483 0.5419 0.5394 0.5268 0.5243 0.5060 0.5031 0.4727 0.4699 0.4201 0.4172 0.3948 0.3942 0.3931 0.3921 0.3900 0.3888 0.3848 0.3834 0.3776 0.3761 0.3662 0.3647 0.3491 0.3474 0.3219 0.3201 0.2723 0.2703 0.2484 0.2481 0.2472 0.2467 0.2451 0.2445 0.2419 0.2412 0.2369 0.2361 0.2293 0.2285 0.2177 0.2170 0.1983 0.1975 0.1621 0.1612

IRDW 0.8022 0.7950 0.7861 0.7719 0.7531 0.7279 0.6941 0.6514 0.5903 0.5582 0.5542 0.5469 0.5379 0.5248 0.5047 0.4780 0.4365 0.3740 0.3926 0.3897 0.3851 0.3782 0.3690 0.3547 0.3338 0.3010 0.2448 0.2476 0.2460 0.2432 0.2394 0.2337 0.2249 0.2117 0.1899 0.1497

W. Panichkitkosolkul et.al

Silpakorn U Science & Tech J Vol.6(1), 2012

Table 7 The estimated coverage probabilities and lengths of confidence intervals CIW , CI RW , CI RDW and

CI IRDW when p = 10% and ω = −3σ ε .

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

100

250

W 0.9404 0.9086 0.8694 0.8100 0.7602 0.6980 0.6238 0.5670 0.5146 0.9308 0.8792 0.7992 0.7038 0.6018 0.5106 0.4416 0.3954 0.3906 0.9092 0.8212 0.6926 0.5324 0.4032 0.2986 0.2276 0.2166 0.2742 0.8782 0.6698 0.4206 0.2100 0.0870 0.0384 0.0228 0.0266 0.0756

Coverage probabilities RW RDW 0.9550 0.9580 0.9292 0.9444 0.9050 0.9130 0.8566 0.8736 0.8140 0.8236 0.7586 0.7678 0.6924 0.6976 0.6312 0.6374 0.5706 0.5700 0.9438 0.9538 0.8990 0.9204 0.8312 0.8576 0.7434 0.7716 0.6506 0.6742 0.5578 0.5900 0.4850 0.5098 0.4298 0.4426 0.4074 0.4200 0.9198 0.9396 0.8426 0.8744 0.7208 0.7700 0.5636 0.6170 0.4330 0.4758 0.3256 0.3538 0.2512 0.2768 0.2332 0.2538 0.2794 0.2986 0.8892 0.9274 0.6876 0.7676 0.4426 0.5220 0.2260 0.2816 0.0952 0.1258 0.0428 0.0540 0.0252 0.0328 0.0278 0.0352 0.0768 0.0890

IRDW 0.9374 0.9434 0.9352 0.9146 0.8920 0.8558 0.8202 0.7760 0.7374 0.9332 0.9296 0.9036 0.8568 0.8030 0.7466 0.6938 0.6442 0.6348 0.9292 0.9048 0.8498 0.7438 0.6436 0.5424 0.4962 0.4830 0.5388 0.9270 0.8360 0.6428 0.4260 0.2606 0.1606 0.1268 0.1412 0.2692

W 0.8026 0.8006 0.7960 0.7894 0.7780 0.7611 0.7387 0.7069 0.6609 0.5601 0.5581 0.5548 0.5490 0.5402 0.5262 0.5071 0.4747 0.4235 0.3936 0.3921 0.3891 0.3845 0.3773 0.3663 0.3495 0.3220 0.2743 0.2481 0.2470 0.2450 0.2417 0.2368 0.2293 0.2175 0.1983 0.1623

Lengths RW RDW 0.8132 0.8117 0.8106 0.8087 0.8047 0.8023 0.7967 0.7937 0.7835 0.7811 0.7654 0.7625 0.7412 0.7373 0.7071 0.7043 0.6592 0.6558 0.5633 0.5623 0.5609 0.5594 0.5572 0.5553 0.5508 0.5485 0.5417 0.5394 0.5268 0.5242 0.5069 0.5038 0.4736 0.4708 0.4211 0.4184 0.3947 0.3941 0.3930 0.3921 0.3899 0.3887 0.3851 0.3838 0.3776 0.3761 0.3664 0.3648 0.3492 0.3476 0.3212 0.3196 0.2730 0.2710 0.2484 0.2481 0.2473 0.2468 0.2452 0.2445 0.2418 0.2411 0.2368 0.2361 0.2293 0.2286 0.2174 0.2166 0.1980 0.1973 0.1619 0.1610

IRDW 0.8024 0.7958 0.7852 0.7719 0.7533 0.7266 0.6928 0.6505 0.5904 0.5586 0.5535 0.5473 0.5376 0.5247 0.5049 0.4787 0.4374 0.3756 0.3925 0.3895 0.3850 0.3786 0.3689 0.3550 0.3341 0.3006 0.2454 0.2476 0.2460 0.2433 0.2394 0.2335 0.2250 0.2114 0.1897 0.1495

Silpakorn U Science & Tech J Vol.6(1), 2012

Confidence Intervals for the Parameter of a Gaussian First-Order

Table 8 The estimated coverage probabilities and lengths of confidence intervals CIW , CI RW , CI RDW and

CI IRDW when p = 10% and ω = 5σ ε .

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.9484 0.8882 0.8018 0.6686 0.5226 0.3980 0.3120 0.2530 0.2062 0.9212 0.7968 0.6134 0.4310 0.2736 0.1656 0.0972 0.0678 0.0868 0.8754 0.6768 0.4132 0.1946 0.0710 0.0250 0.0088 0.0050 0.0132 0.7864 0.3898 0.0880 0.0100 0.0010 0.0000 0.0000 0.0000 0.0000

100

250

Coverage probabilities RW RDW 0.9602 0.9154 0.8490 0.7356 0.5932 0.4696 0.3754 0.3092 0.2468 0.9340 0.8274 0.6564 0.4698 0.3126 0.1922 0.1166 0.0860 0.0966 0.8914 0.7028 0.4372 0.2138 0.0800 0.0302 0.0100 0.0060 0.0150 0.7992 0.4066 0.0948 0.0108 0.0010 0.0000 0.0000 0.0000 0.0000

0.9618 0.9336 0.8750 0.7748 0.6358 0.4960 0.3904 0.3196 0.2596 0.9566 0.8890 0.7420 0.5430 0.3630 0.2242 0.1334 0.0996 0.1106 0.9390 0.8086 0.5640 0.3166 0.1260 0.0536 0.0164 0.0094 0.0222 0.9212 0.6232 0.2096 0.0322 0.0020 0.0000 0.0000 0.0000 0.0002

Lengths RDW

IRDW

0.9568 0.9452 0.9146 0.8394 0.7458 0.6524 0.5650 0.5074 0.4450 0.9482 0.9134 0.8100 0.6576 0.5078 0.3808 0.2842 0.2462 0.2858 0.9338 0.8512 0.6538 0.4336 0.2342 0.1352 0.0782 0.0656 0.1198 0.9220 0.6916 0.3006 0.0710 0.0112 0.0014 0.0010 0.0004 0.0050

0.8032 0.8030 0.8020 0.7999 0.7964 0.7902 0.7790 0.7611 0.7362 0.5604 0.5601 0.5592 0.5574 0.5542 0.5488 0.5400 0.5230 0.4875 0.3939 0.3936 0.3927 0.3909 0.3885 0.3837 0.3763 0.3609 0.3269 0.2483 0.2480 0.2474 0.2463 0.2445 0.2415 0.2358 0.2249 0.1988

0.8107 0.8097 0.8083 0.8054 0.8012 0.7949 0.7826 0.7640 0.7381 0.5625 0.5620 0.5611 0.5589 0.5555 0.5497 0.5405 0.5229 0.4867 0.3947 0.3943 0.3932 0.3914 0.3889 0.3839 0.3764 0.3607 0.3261 0.2485 0.2482 0.2475 0.2464 0.2445 0.2416 0.2358 0.2248 0.1985

0.8092 0.8081 0.8060 0.8031 0.7988 0.7918 0.7796 0.7605 0.7343 0.5612 0.5603 0.5589 0.5565 0.5526 0.5465 0.5375 0.5193 0.4824 0.3939 0.3930 0.3918 0.3895 0.3868 0.3816 0.3739 0.3583 0.3234 0.2480 0.2474 0.2465 0.2453 0.2433 0.2401 0.2344 0.2235 0.1973

IRDW 0.8046 0.8019 0.7974 0.7921 0.7844 0.7720 0.7527 0.7230 0.6845 0.5592 0.5573 0.5551 0.5514 0.5454 0.5361 0.5225 0.4966 0.4459 0.3930 0.3917 0.3901 0.3869 0.3831 0.3762 0.3656 0.3448 0.3005 0.2477 0.2470 0.2459 0.2445 0.2420 0.2382 0.2314 0.2181 0.1870

W. Panichkitkosolkul et.al

Silpakorn U Science & Tech J Vol.6(1), 2012

Table 9 The estimated coverage probabilities and lengths of confidence intervals CIW , CI RW , CI RDW and

CI IRDW when p = 10% and ω = −5σ ε .

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

100

250

W 0.9494 0.8956 0.7950 0.6864 0.5244 0.4102 0.3246 0.2456 0.2100 0.9272 0.7976 0.6264 0.4282 0.2678 0.1694 0.1006 0.0664 0.0872 0.8824 0.6756 0.4158 0.1986 0.0778 0.0260 0.0086 0.0070 0.0182 0.7900 0.3878 0.0884 0.0122 0.0008 0.0000 0.0000 0.0000 0.0000

Coverage probabilities RW RDW 0.9630 0.9672 0.9236 0.9356 0.8426 0.8808 0.7500 0.7830 0.5912 0.6300 0.4800 0.5006 0.3878 0.4050 0.2980 0.3084 0.2534 0.2660 0.9370 0.9594 0.8284 0.8838 0.6674 0.7422 0.4698 0.5532 0.3036 0.3598 0.1974 0.2312 0.1216 0.1500 0.0780 0.0988 0.0972 0.1150 0.8980 0.9416 0.7070 0.8144 0.4416 0.5712 0.2168 0.3060 0.0882 0.1258 0.0318 0.0466 0.0108 0.0184 0.0084 0.0110 0.0202 0.0278 0.8004 0.9164 0.4036 0.6148 0.0968 0.2144 0.0134 0.0354 0.0008 0.0040 0.0000 0.0006 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

IRDW 0.9620 0.9470 0.9146 0.8464 0.7538 0.6524 0.5782 0.4954 0.4520 0.9518 0.9072 0.8148 0.6752 0.5126 0.3894 0.2988 0.2588 0.2810 0.9354 0.8568 0.6638 0.4284 0.2270 0.1264 0.0742 0.0722 0.1248 0.9166 0.6814 0.3026 0.0782 0.0132 0.0024 0.0008 0.0012 0.0060

W 0.8042 0.8036 0.8024 0.8000 0.7964 0.7906 0.7783 0.7627 0.7338 0.5608 0.5600 0.5590 0.5573 0.5542 0.5487 0.5399 0.5226 0.4873 0.3940 0.3936 0.3926 0.3911 0.3885 0.3839 0.3762 0.3606 0.3268 0.2483 0.2480 0.2473 0.2463 0.2444 0.2413 0.2358 0.2246 0.1986

Lengths RW RDW 0.8114 0.8103 0.8101 0.8085 0.8087 0.8069 0.8055 0.8028 0.8016 0.7989 0.7948 0.7920 0.7817 0.7783 0.7655 0.7615 0.7357 0.7315 0.5628 0.5616 0.5620 0.5602 0.5608 0.5587 0.5588 0.5563 0.5555 0.5529 0.5498 0.5466 0.5405 0.5370 0.5225 0.5185 0.4863 0.4818 0.3947 0.3939 0.3942 0.3930 0.3931 0.3916 0.3915 0.3897 0.3889 0.3869 0.3841 0.3819 0.3762 0.3739 0.3603 0.3580 0.3260 0.3234 0.2485 0.2480 0.2481 0.2474 0.2475 0.2465 0.2464 0.2452 0.2445 0.2432 0.2414 0.2400 0.2358 0.2344 0.2245 0.2233 0.1983 0.1970

IRDW 0.8060 0.8025 0.7989 0.7917 0.7844 0.7728 0.7515 0.7245 0.6817 0.5596 0.5573 0.5548 0.5511 0.5455 0.5358 0.5220 0.4951 0.4459 0.3930 0.3918 0.3898 0.3872 0.3834 0.3766 0.3657 0.3446 0.3004 0.2477 0.2470 0.2459 0.2444 0.2419 0.2381 0.2312 0.2180 0.1865

Silpakorn U Science & Tech J Vol.6(1), 2012

Confidence Intervals for the Parameter of a Gaussian First-Order

Discussions and Conclusions

An Empirical Application To illustrate the empirical application of the

In this paper, we have compared the interval

confidence intervals which have been proposed

estimation of the parameter for a Gaussian first-

in the previous section, we have used the yearly

order autoregressive model with additive outliers.

real exchange rates between the USA and Mexico

The confidence intervals considered in this study are based on the weighted symmetric estimator ( φˆ ),

from 1970 to 2009 (base year is 2005). The series

giving a total of 40 observations was collected from

the recursive mean adjusted weighted symmetric estimator ( φˆRW ), the recursive median adjusted weighted symmetric estimator ( φˆ ), and the

the Economic Research Service, United States Department of Agriculture. The time series plot,

RDW

the sample autocorrelation function (ACF) and the sample partial autocorrelation function (PACF), as

improved recursive median adjusted weighted symmetric estimator ( φˆ ). Using the simulations,

shown in Figures 1 and 2, suggest that an AR(1)

we compare the coverage probability and length of

model is suitable for this series. We detected the

the confidence intervals. For all sample sizes, the

additive outliers of this series by using an iterative

percentages of additive outliers and the magnitudes

detecting procedure proposed by Chang et al. (1988)

of the additive outliers, the confidence interval based on the estimator φˆIRDW assigns more value to

IRDW

via the R statistical software (see, for example, Cryer and Chan, 2008, pp.257-259 and pp.455). We

coverage probabilities than the confidence intervals based on the estimators φˆ , φˆ and φˆ in almost

found an additive outlier at t = 12 (year 1981) and

RDW

intervals for an autoregressive parameter which

all φ values. So, we can conclude that the confidence interval based on the estimator φˆ is superior to the

they are displayed in Table 10. As can be seen from

other confidence intervals in terms of the coverage

Table 10, the CI IRDW provides the length shorter

probabilities and lengths when autoregressive

than those of the CIW , CI RW and CI RDW . The real

time series contaminated with additive outliers.

we also compute the estimates and the confidence

IRDW

application in this section confirms that the CI IRDW is much better than the other confidence intervals.

W. Panichkitkosolkul et.al

Silpakorn U Science & Tech J Vol.6(1), 2012

Figure 1 The US/Mexico of real exchange rates; annual from 1970 to 2009

Figure 2 ACF and PACF of the US/Mexico of real exchange rates

Silpakorn U Science & Tech J Vol.6(1), 2012

Confidence Intervals for the Parameter of a Gaussian First-Order

Table 10 The estimates and the confidence intervals for the first-order autoregressive parameter of the US/ Mexico of real exchange rates series Methods

Estimates

W RW RDW IRDW

0.7874 0.7821 0.8378 0.8971

Confidence intervals Lower limits Upper limits 0.5964 0.9784 0.5911 0.9731 0.6738 1.0017 0.7663 1.0278

Acknowledgements

Lengths 0.3820 0.3820 0.3279 0.2614

Guo, J. H. (2000) Robust estimation for the

The authors would like to thank two

coefficient of a first order autoregressive

anonymous referees for their valuable suggestions

process. Communications in Statistics-Theory

and constructive comments which were helpful in

and Methods 29: 55-66.

improving this paper. The authors also wish to thank

Mann, H. B., and A. Wald. (1943) On the statistical

Mr. Panchai Poonwathu for his careful reading.

treatment of linear stochastic difference equations. Econometrica 11: 173-220.

References

Marriott, F. H. C., and J. A. Pope. (1954) Bias in the estimation of autocorrelations. Biometrika

Abraham, B., and G. E. P. Box. (1979) Bayesian analysis of some outliers problems in time

41: 390-402.

series. Biometrika 66: 229-236.

Martin, R. D. (1980) Robust estimation of

Brockwell, P. J., and R. A. Davis. (1991) Time

autoregressive models. In Directions in Time

Series: Theory and Methods. Springer, New

Series (Brillinger, D. R. and Tiao, G. C.,

York.

eds) pp.228-254. Institute of Mathematical

Chang, I., G. C. Tiao, and C. Chen. 1988. Estimation

Statistics, California.

of time series parameters in the presence of

Newbold, P., and C. Agiakloglou. (1993) Bias in

outliers. Technometrics 30: 193-204.

the sample autocorrelations of fractional noise.

Chatfield, C. (2001) Time-Series Forecasting.

Biometrika 80: 698-702. Niwitpong, S. (2007) Predictive Inference for Time

Chapman & Hall, New York. Conover, W. J. (1980) Practical Nonparametric

Series. Ph.D. Dissertation. La Trobe University,

Statistics. John Wiley & Sons, New York.

Bundoora, Victoria, Australia.

Cryer, J. D., and K. S. Chan. (2008) Time Series

Panichkitkosolkul, W. (2010a) New estimator for

Analysis with Application in R. Springer, New

an unknown mean Gaussian AR(1) process

York.

with additive outliers. Chiang Mai Journal of Science 37: 14-20.

Denby, L., and R. D. Martin. (1979) Robust estimation of the first-order autoregressive

Panichkitkosolkul, W. (2010b) An improved

parameter. Journal of the American Statistical

estimator for a Gaussian AR(1) process with an

Association 74: 140-146.

unknown drift and additive outliers. Thailand

Fox, A. J. (1972) Outliers in time series. Journal of

Statistician 8: 1-15.

the Royal Statistical Society 34: 350-363.

Park, H. J., and W. A. Fuller. (1995) Alternative

W. Panichkitkosolkul et.al

Silpakorn U Science & Tech J Vol.6(1), 2012

Probability Letters 43: 65-73.

estimators and unit root tests for the

The R Development Core Team. (2010a) An

autoregressive process. Journal of Time Series

Introduction to R. R Foundation for Statistical

Analysis 16: 415-429.

Computing, Vienna.

Shaman, P., and R. A. Stine. (1988) The bias of autoregressive coefficient estimators. Journal

The R Development Core Team. (2010b) R: A

of the American Statistical Association 83:

Language and Environment for Statistical

842-848.

Computing. R Foundation for Statistical Computing, Vienna.

So, B. S., and D. W. Shin. (1999) Recursive mean adjustment in time series inferences. Statistics

Research Article Preparation of Pectin from Fruit Peel of Citrus maxima Uthai Sotanaphun 1*, Amornrut Chaidedgumjorn 2, Nudchanart Kitcharoen 1, Malai Satiraphan 2, Panida Asavapichayont 3 and Pornsak Sriamornsak 3 1

Department of Pharmacognosy, 2 Department of Pharmacetuical Chemistry, 3 Department of Pharmaceutical Technology, Faculty of Pharmacy, Nakhon Pathom, Thailand * Corresponding author. E-mail address: uthai@su.ac.th Received July 30, 2011; Accepted October 7, 2011

Abstract The extraction of high-methoxyl pectin from the fruit peel of Citrus maxima was studied. The suitable condition was the extraction at 80 °C without pH adjustment (pH was about 4.5) in 20 times by volume of water. For up-scale procedure, the peel was pre-soaked in water for overnight to wash out small molecular water-soluble substances. Amberlite XAD-16 polystyrene was used to remove phenolic compounds before concentration and precipitation of pectin. This suggested method was simple and inexpensive. The yield of the obtained pectin was 7.23±0.19%. Its galacturonic acid content and degree of esterification were 74.12±2.07% and 76.30 ±3.38%, respectively. Key Words: Citrus maxima; Galacturonic acid; High-methoxyl pectin; Pomelo; Up-scale production Introduction Pectin is a polysaccharide widely used in food and pharmaceutical industries. It is used as thickening and gelling agents (May, 1990). Its medical uses are antidiarrhea, detoxification and blood glucose lowering (Voragen et al., 1995). Pectin consists of a linear backbone of linked d-galacturonic acid units and branched region of neutral sugars. The carboxyl group of galacturonic acid can be free or methyl-esterified which classifies pectin into high- and low- methoxyl types depending on their degree of esterification (Voragen et al., 1995; Novosel’skaya et al., 2000; Willats et al., 2001). Fruit peels of Citrus such as orange, lemon and lime, are well recognized as conventional sources of commercial pectin (Rolin, 1993).

Silpakorn U Science & Tech J 6 (1) : 42-48, 2012

Classically, two main production steps of pectin include extraction from raw material with water and isolation of pectin from the extracted solution by precipitation with alcohol (May, 1990; Rolin, 1993; Voragen et al., 1995; Kalapathy et al., 2001; Joye and Luzio, 2000). Commercial pectin is extracted at high temperature by hydrolyzing protopectin using acid (May, 1990; Minkov, 1996). In general, higher yield is obtained from high temperature and low pH extraction. In contrast, molecular weight and degree of esterification (DE) will be decreased (Joy and Luzio, 2000). Therefore, the suitable condition for each kind of raw material needs to be optimized. Our previous study showed that pomelo or Citrus maxima (Family Rutaceae), one of the popular fruit of Thailand, could be used as a source of high-

U. Sotanaphun et al.

Silpakorn U Science & Tech J Vol.6(1), 2012

Extraction Conditions of Pectin Dried peel of C. maxima (100 g) was extracted with water (2,000 mL x 2 times) at different pHs (2, 3 and 4.5) and temperatures (30, 50, 80 and 100°C) for 3 hours. The extract was concentrated under reduced pressure to the final volume of 200 mL. It was further dialyzed (D9527, Sigma-Aldrich, St. Louis, Missouri, USA) for 1 hour, repeated 8 times. Pectin was precipitated by adjusting pH to 3.5 and adding double volume of 95% ethanol. After centrifugation at 3,500 rpm for 8 min and washing with 95% ethanol, pectin was collected and dried at 50°C. Purification Methods of Pectin Dried peel of C. maxima (100 g) was extracted with water (2,000 mL x 2 times) at 80°C and pH 4.5. Five purification methods were compared (Table 1). Dialysis was the reference method (method A).

methoxyl pectin (Chaidedgumjorn et al., 2009). Its fruit is fairly large and considerable amount of the peel is biological waste. The aim of this study was to investigate the optimum condition for the extraction of high-methoxyl pectin from this waste. The development of a simple up-scale procedure was also suggested. Experimental Materials Mature fruits of Citrus maxima (Burm. f.) Merr. cultivar Khao-nam-phueng were harvested from Nakhon-Pathom province, Thailand, during 2005. They were stored at room temperature (30°C) for 30 days before using in the experiment. Fruit peels (outer green layer and inner white layer) were cut into a cube size approximately 4x4x4 mm3 and dried at 50°C in hot-air oven.

Table 1 Yield and general properties of pectin prepared from different purification methods: (A) = dialysis, (B) = pretreatment in water, (C) = pretreatment + washing pectin with EtOH, (D) = pretreatment + washing pectin with HCl/EtOH, and (E) = pretreatment + XAD16 Method

Extraction cycle

Yield [Total yield] (% w/w)

Galacturonic acid (%)

Viscosity (centipoises)1

pH2

1st

4.73 ± 0.13a

73.23 ± 1.55a

12.16 ± 0.06a

3.69 ± 0.03a

2nd

4.10 ± 0.25a,b

73.43 ± 0.63a

8.09 ± 0.40

3.66 ± 0.04a

[8.84 ± 0.39c] B

1st

11.41 ± 0.30

41.05 ± 0.94

2.90 ± 0.00b

4.56 ± 0.02b,c

2nd

6.60 ± 0.02

54.18 ± 0.05

2.91 ± 0.23b

5.62 ± 0.07d

[18.01 ± 0.28] C

1st

4.40 ± 0.06a,d

61.62 ± 0.45b

11.64 ± 0.19a

5.72 ± 0.42d

3.89 ± 0.23

62.82 ± 0.06

8.82 ± 0.01

4.86 ± 0.01b

b,d,e

[8.28 ± 0.30c,f] D

1st

3.75 ± 0.03b,d,e

69.49 ± 0.61

18.00 ± 0.39

4.32 ± 0.03c

2nd

3.76 ± 0.06 b,d,e

72.94 ± 0.29

13.05 ± 0.07

3.76 ± 0.01a

[7.51 ± 0.03f] E

1st

5.61 ± 0.23

65.70 ± 0.23

10.58 ± 0.24

3.83 ± 0.00a

2nd

3.20 ± 0.78e

71.41 ± 1.57

9.28 ± 0.69c

3.74 ± 0.01a

[8.81 ± 1.01 ] c

Viscosity of the 1% w/w solution at 25°C. 2pH at 1% w/w solution. significant difference (p ≥ 0.05). 1

a-e

Same letters within a column indicate no

Silpakorn U Science & Tech J Vol.6(1), 2012

Preparation of Pectin from Fruit Peel of Citrus Maxima

Figure 1 Yield and general properties of pectin extracted from different conditions ( = first extraction cycle, = second extraction cycle. a-e Same letters within a graph indicate no significant difference (p â&#x2030;Ľ 0.05). Quality of pectin from the first extraction cycle at pH4.5 and 50Â°C could not be determined because it did not dissolve in water.)

U. Sotanaphun et al.

Silpakorn U Science & Tech J Vol.6(1), 2012

For the other four methods, the peel was soaked in water for overnight and filtered before using for the extraction. After precipitation, the extracted pectin was either directly collected by filtration through cheese cloth (method B) or centrifugation and washing. Pectin from method C was washed with 70-95% ethanol, whereas method D used hydrochloric solution (pH 2) and followed with 7095% ethanol. Amberlite XAD-16 polystryrene resin (06442, Fluka Chemika, Switzerland) was used in method E to purify the extracted solution before pectin precipitation. Up-Scale Extraction of Pectin Dried peel of C. maxima (1 kg) was pretreated by soaking in water (20 L) at room temperature (30°C) for 18 hours (overnight). Then the peel was filtered and pressed, and further extracted with water (20 L) at 80°C for 2 times (4.5 and 5.5 hours) in an electric ern (Satien Stainless Steel public company limited, Thailand). The combined extract was filtered through an Amberlite XAD-16 polystryrene resin (1 kg) to remove phenolic compounds. The extract was concentrated to about 500 mL and pH adjusted to 3.5. Then 95% ethanol (1 L) was added to precipitate pectin. Pectin coagulation was filtered through cheese cloth, dried at 50°C and ground to powder. Analysis of Galacturonic Acid, Degree of Esterification and Viscosity of Pectin Solution. Galacturonic acid content and degree of esterification were determined by the titration method (USP 26-NF21, 2002). The apparent viscosity of 1.0 %w/w pectin solution was determined using a Brookfield digital viscometer model RV DV-1 (Brookfield Engineering Laboratories, Inc., USA) with an UL adaptor at 25oC and a speed of 20 rpm.

(Chaidedgumjorn et al, 2009). Some extractive conditions were varied to investigate the effect of pH and temperature. The results are shown in Figure 1. At low pH and high temperature a larger amount of extracted pectin was obtained. The highest yield (11.91%) was the extraction at pH2 and 80°C for 2 extraction cycles. However its low %galacturonic acid content (55.04-56.25%) indicated that pectin was mixed with other constituents. Purity of pectin or galacturonic acid content depended on pH, whereas the effect of temperature was not clear. A higher %galacturonic acid was obtained with the increasing of pH. In contrast, high viscosity products were obtained when using low pH condition. Extraction at pH2 and 50°C gave the high viscosity products (82.29-221.87 centipoises at 1% solution), but its %galacturonic acid was low (55.02-55.67%). It was suggested that pectin along with other polymers were extracted at this low pH condition. These unknown polymers might be responsible for the high viscosity property, since the molecular weight of pectin from C. maxima was low (Chaidedgumjorn et al, 2009). A little higher pH of this product (pH 5.12-5.81) also confirmed the low purity because pectin is acidic in nature. Viscosity was strongly affected by temperature. The increase in temperature might shorten the polymer chain and decreased its viscosity property as reported for pectin extracted from other sources (Joye and Luzio, 2000). Based on all above information, pH 4.5 and 80°C was suggested as the suitable condition for the extraction of water-soluble pectin from C. maxima. The pH 4.5 is the natural acidity produced by acid composition in the peel. A similar method using natural pH has been reported for the extraction of pectin from lemon peel (Ehrlich, 1997). The yield from this condition with repeated 2 extraction cycles (8.84%) was not different from that previously reported (Huong and Luyen, 1989), but a better quality in terms of viscosity was obtained. To scale-up the extraction, purification using dialysis was not likely possible. Our preliminary

Results and Discussion The peel (both green and white layers) of C. maxima cultivar Khao-nam-phueng, stored for 30 days after harvesting, was used for the extraction of water-soluble pectin or high-methoxyl pectin 45

Silpakorn U Science & Tech J Vol.6(1), 2012

Preparation of Pectin from Fruit Peel of Citrus Maxima

examination indicated that a number of watersoluble small molecular molecules could be removed before pectin extraction by soaking the peel in water at room temperature (30°C) overnight. This method was based on the principle that solubility of small molecules in water, in general, is better than large molecules. A similar method (washing the material with water before pectin extraction) has been reported for beet root (Wang and Chang, 1994). However, even the peel was pretreated in water (method B in Table 1), phenolic compounds, especially flavonoids, were still present in the extracted pectin. Washing pectin with aqueous ethanol is a method that often used for removing non-polar to polar small molecules (Voragen et al., 1995). In this study, extracted pectin was washed with 70% and 95% ethanol until it gave negative test to phenolics and flavonoids (detected with FeCl3 TS. and Shibata’s test, respectively). As shown in Table 1, its galacturonic content was improved (comparing method C to method B), but it was still lower than the typical requirements of 65% (May, 1990) and far from pharmaceutical standard at 74% (USP 26NF21, 2002). Washing pectin with acidic aqueous ethanol was the other reported method (Ali et al., 2003). Pectin from this method possessed acceptable %galacturonic acid (method D in Table 1). However, it needed repeating washing-centrifugation process which was not suitable for the production scale. The efficiency of polymeric resin to remove phenolic compounds from pectin was proven (Schieber et al, 2003). In this study, Amberlite XAD-16 polystyrene was used. Pectin solution was passed over the resin which was covered with cheese cloth and placed on a flour sieve. This technique was better than packing the resin in a column because it was not clogged by some gelling particles in pectin solution. One kilogram of Amberlite XAD-16 was sufficient for pectin solution that prepared from 1 kilogram of the peel. Purity of pectin from this method was closed to the requirement value. Its viscosity and

pH were also not different from that prepared from dialysis method (Table 1, comparing method E to method A). Moreover, the advantage of Amberlite XAD-16 is that it can be re-used by re-activation with alcohol. The concentration technique before pectin precipitation is also concerned. Concentration under reduce pressure is time consuming and uses expensive instrument. Concentration by boiling a volume of pectin solution in a wide tray over a hot-plate for not more than 1 hour could be used as a simple and fast method. But viscosity of pectin was found to decrease. The up-scale production was tested on 1 kilogram of the peel. In order to achieve the same solution concentrations as those of the laboratory scale by measuring total soluble solids (approximate 1.0 and 0.5°Brix for the first and second extraction cycles), we found that extraction time needed be increased from 3 and 3 hours each to 4.5 and 5.5 hours, respectively. Conclusion This study investigated the effects of temperature and pH on the extraction of pectin from the fruit peel of Citrus maxima. The up-scale extraction process also suggested and concluded in Figure 2. Data of three production batches revealed some variation in yield and quality. The extraction yield was 7.23±0.19%. The viscosity of 1% solution was 4.52±1.36 centipoises. The galacturonic acid content was 74.12±2.07%, and the degree of esterification was 76.30±3.38%, clearly indicated that the extracted pectin was high-methoxyl pectin. Acknowledgement This work was financially supported by Silpakorn University Research and Development Institute, under the research program “Production of pectin from pomelo (Citrus maxima) peel and application in pharmaceutical industry”.

U. Sotanaphun et al.

Silpakorn U Science & Tech J Vol.6(1), 2012

C. maxima fruit peel

(1) Pretreatment

Soaking in water to remove small molecular water soluble substances.

(2) Extraction

Boiling in water at 80°C.

Pectin solution (3) Purification Adsorption of phenolic compounds with Amberlite XAD-16.

(4) Concentration and Evaporation in a wide tray on hot-plate. precipitation Precipitation with alcohol. High-methoxyl pectin

Figure 2 Flow diagram of the up-scale extraction of pectin from C. maxima fruit peel

References Ali Sahari, M., Ali Akbarian, M., and Manuchehr, H. (2003) Effect of variety and acid washing method on extraction yield and quality of sunflower head pectin. Food Chemistry 83(1): 43-47. Chaidedgumjorn, A., Sotanaphun, U., Kitcharoen, N., Asavapichayont, P., Satiraphan, M., and Sriamornsak, P. (2009) Pectins from Citrus maxima. Pharmaceutical Biology 47(6): 521–526. Ehrlich, R. M. (1997) Method for making pectin and pectocellulosic products. United States Patent 5,656,734. Aug 12. Huong, D. M., and Luyen, D. V. (1989) Optimization of pectin extraction from dried peel of Citrus grandis. Polymer Bulletin 22(5-6): 599-602.

material by differential pH. Carbohydrate Polymers 43(4): 342-337 Kalapathy, U., and Proctor, A. (2001) Effect of acid extraction and alcohol precipitation conditions on the yield and purity of soy hull pectin. Food Chemistry 73(4): 393-396. May, C. D. (1990) Industrial pectins: sources, production and applications. Carbohydrate Polymers 12(1): 79-99. Minkov, S., Minchev, A., and Paev, K. (1996) Modelling of the hydrolysis and extraction of apple pectin. Journal of Food Engineering 29(1): 107–113. Novosel’skaya, I. L., Voropaeva, N. L., Semenova, L. N., and Rashidova, S. Sh. (2000) Trends in the science and application of pectins. Chemistry of Natural Compounds 36(1): 1-10.

Joye, D. D., and Luzio, G. A. (2000) Process for selective extraction of pectins from plant

Rolin, C. (1993) Pectin. In Industrial Gums: Polysaccharides and Their Derivatives. 47

Silpakorn U Science & Tech J Vol.6(1), 2012

Preparation of Pectin from Fruit Peel of Citrus Maxima

(Whistler, R. L., and BeMiller, J. N., eds.), pp. 258-293. Academic Press, New York. Schieber, A., Hilt, P., Streke, P., Endreb, H.U., Rentschler, C., and Carle, R. (2003) A new process for the combined recovery of pectin and phenolic compounds from apple pomace. Innovative Food Science & Emerging Technologies 4(1): 99-107. United States Pharmacopeial Convention. (2002) The United States Pharmacopeia-The National Formulary (USP 26-NF21). pp. 1401-1402. Webcom Limited, Toronto.

Voragen, A. G. J., Pilnik, W., Thibault, J. F., Axelos, M. A. V., and Renard, C. M. G. C. (1995) Pectins. In Food Polysaccharides and Their Applications. (Stephen A. M., edt.), pp. 287369. Marcel Dekker, New York. Wang, C. C. H., and Chang, K. C. (1994) Beet pulp and isolated pectin physiochemical properties as related to freezing. Journal of Food Science 59(6): 1153-1154. Willats, W. G. T., McCartney, L., Mackie, W., and Knox, J. P. (2001) Pectin: cell biology and prospects for function analysis. Plant Molecular Biology 47(1-2): 9-27.

Research Article Development of Instant Rice for Young Children Bencharat Prapluettrakul 1, Patcharee Tungtrakul 2, Sukamol Panyachan 1 and Tasanee Limsuwan 1* Department of Home Economics, Faculty of Agriculture, 2 Institute of Food Research and Product Development, Kasetsart University, Bangkaen Campus. Bangkok, Thailand * Corresponding author. E-mail address: tasaneelim50@hotmail.com 1

Received September 28, 2011; Accepted February 12, 2012 Abstract The objective of this research was to find a suitable method for producing an instant rice product from Thai Jasmine rice for young children aged 1-3 years old. Different methods of rice cooking, pre-treatment prior to drying, and rehydration were studied. Volume expansion, rehydration ratio, rehydration time, colour, texture, and sensory characteristics of instant rice product were compared. The results showed that the instant rice product prepared by boiling followed by freezing for 24 h at –20 ºC, drying at 70 ºC, and rehydration by boiling for 3 min showed no significant difference in hardness, adhesiveness, or cohesiveness from the freshly cooked rice. The hardness, adhesiveness and cohesiveness were 349.75 ± 3.94 N, –23.09 ± 1.30 N.s, and 0.49 ± 0.01, respectively. The sample also received the highest scores for stickiness, softness, and overall acceptability for use as food for young children. Boiling followed by 24 h of freezing prior to drying is recommended for producing instant rice for young children. Key Words: Instant food; Rice; Young children Introduction Rice is the staple food for over half the world’s population, including the Thai population. Khao Dawk Mali 105 or Thai Jasmine Rice is the most popular variety for consumption in Thailand because of its pleasant fragrance when cooked as well as its good texture. Rice is also a suitable food for young children because it is easy to digest; it contains many essential nutrients and no gluten. The recommended diet for babies for the first six months is mother’s milk exclusively, after which complementary foods may be introduced in addition to mother’s milk. Traditionally in Thailand the popular complementary foods are mashed banana and mashed rice porridge. Young children aged one

Silpakorn U Science & Tech J 6 (1) : 49-58, 2012

to three years rely more on staple foods like cooked rice or rice porridge that is not mashed so they can get used to chewing soft rice. Most Thai families prepare their own children’s food. However, these days many families do not have time to prepare their own young children’s food and prefer to buy ready prepared food products that are convenient to serve. Many families also rely on child care centers to supply their young children’s nutrition. A preliminary survey of the foods for young children available on the market showed that the selection is limited. Most are instant products that have a liquid or paste-like consistency when rehydrated. These types are suitable in the early stages when babies are first given complementary food but are not suitable

Silpakorn U Science & Tech J Vol.6(1), 2012

Development of Instant Rice for Young Children

for young children. The other instant rice products on the market are also mostly not intended for young children. Previous investigations have proposed instant rice preparation processes consisting of methods of soaking, cooking, pre-treatment prior to drying, drying, and rehydration. The method of soaking, boiling, washing prior to freezing, and drying was suggested by Kongseree et al. (2002). Rewthong et al. (2011) suggested that the boiling method for cooking rice was better than the application of electric rice cooker and washing step prior to freezing gave poorer eating quality. The washing step prior to freezing was shown to be unnecessary for instant rice cooked by boiling (Carlson et al.,1979). It has also been reported that the texture of many rehydrated instant rice products is harder and less chewy than freshly cooked rice (Luangmalawat et al., 2008). None of the previous research specified use for young children. Therefore, the objective of this research was to find a suitable method to produce an instant rice

product from Thai Jasmine rice for young children by comparing the methods previously reported. Such a product would be helpful for families and nurseries or child centers that require rice which can be prepared quickly for young children, and it would also provided added value to Thai Jasmine rice. Materials and Methods Materials The raw material for all the experiments was Thai Jasmine rice purchased from a local distributor in Bangkok. Preparation of Instant Rice Five hundred grams of uncooked Thai Jasmine rice was pre-washed with water before cooking, then water was added at the ratio of one part rice to 1.5 parts water by volume, and the mixture was left to stand for 10 min. Methods of cooking and preparation of instant rice recommended by previous research (Kongseree et al., 2002; Rewthong et al., 2011) were compared, as shown in Figure 1.

Jasmine rice + water, 1:1.5 v/v

Cooking in an electric rice cooker 22 min +simmering 10 min

Boiling 9 min+ simmering 10 min

Freezing -20 °C. 24 h (P1)

Rinsing in cold water

Freezing -20 °C. 24 h (P2)

(4 °C.) then freezing 2 h (P3)

Drying in a hot air oven 70 °C.

Instant rice

Figure 1 Methods for preparing instant rice

Rinsing in cold water (4 °C.) then freezing 2 h (P4)

T. Limsuwan et al.

Silpakorn U Science & Tech J Vol.6(1), 2012

Two methods of cooking rice were compared: boiling and cooking in an electric rice cooker (Sharp, model KS-11E). Two methods for pre-treatment rice before drying was conducted by 1) freezing at -20 ºC for 24 h and 2) rinsing in cold water for 30 sec and then freezing at -20 ºC for 2 h. The prepared rice was then spread over aluminum drying screens and placed in a hot air dryer (Binder, FD115 model) at 70 ºC until the moisture content was reduced to about 5% by weight. The resulting instant rice product was analysed for moisture content (AOAC, 2000), volume expansion (Kongseree et al., 2002), rehydration ratio, and rehydration time. To find the most appropriate method for rehydration of the resulting instant rice for use as a food for young children, the samples were boiled for 3, 4, or 5 min and then left to simmer for 8 min. After rehydration, the samples were analysed for colour and texture compared to the freshly cooked rice. The sensory evaluation was undertaken by a sensory panel of 10 panelists with experience in preparing food for infants and young children at the Kasetsart University child care center. Quality Evaluation 1. The moisture content of the rehydrated instant rice and freshly cooked Thai Jasmine rice were measured by drying in a hot air oven at 105 ± 2 °C for 6 h, following the method of AOAC (2000). 2. The volume expansion was measured following the method of Kongseree et al. (2002). Twenty grams samples of each instant rice product were placed in a volumetric cylinder and the volume was noted, water at a temperature of 95 ºC was added, and the expanded volume was measured every 2 min for 40 min. Three replications were carried out.

3. The rehydration ratio was measured following the method of Prasert and Suwannaporn (2009). One hundred millilitres of water at 95 ºC were added to 10 g of instant rice. Excess water was dabbed away and the samples were weighed every 2 min for 40 min. After three replications, the water rehydration ratio was calculated thus: Rehydration ratio = weight of instant rice after absorption of water (g) starting dry weight (g) 4. The rehydration time was measured following the method of Kongseree et al. (2002). One hundred grams of each instant rice product were boiled in boiling water, then removed from the water with a sieve spoon, and left to drain. Excess water was dabbed away and the moisture content was measured by heating in a hot air oven (AOAC 2000) and measuring samples once per minute for 10 min. Three replications were carried out. 5. The colour of rehydrated instant rice was compared to that of freshly cooked rice using a Hunter Lab Color Flex colorimeter using the CIE Lab (1976) L*a* and b* system. 6. A texture profile analysis (TPA) was done for the rehydrated instant rice compared to freshly cooked rice, testing for hardness, adhesiveness, and cohesiveness using a method adapted from Kiathanapaiboon (2008) on the TA-XT.plus texture analyser (Stable Micro Systems, UK). Samples of 14 g were placed in the cylindrical blocks and readings were taken with a 100-mm diameter cylindrical probe at the rate of 1.0 mm/sec. Five replications were carried out. Sensory Evaluation The samples were evaluated by 10 panelists using a nine-point hedonic scale. The panelists all have an experience in preparing food for infants and young children at the Kasetsart University child care center.

Volume expansion =

volume of reconstituted product (ml) starting volume (ml)

Silpakorn U Science & Tech J Vol.6(1), 2012

Development of Instant Rice for Young Children

Volume Expansion There was a statistically significant difference in volume expansion among the rice products prepared by the four different methods (p < 0.05). The volume expansion of rice samples which were frozen for 24 h (P1 and P2) was higher than that of samples frozen for 2 h after rinsing with cold water (P3 and P4), as shown in Figure 2.

Statistical Analysis Data obtained from all the tests were analyzed by using one-way analysis of variance (ANOVA) and followed by Duncan multiple range test. Results and Discussion Analysis of the Quality of Instant Rice Products

Figure 2 Volume expansion of instant rice products after reconstitution

P1 = rice boiled + frozen for 24 h P2 = rice cooked in an electric rice cooker + frozen for 24 h P3 = rice boiled + rinsed + frozen for 2 h P4 = rice cooked in an electric rice cooker + rinsed + frozen for 2 h Lu et al. (1997) and Mohamed et al. (2006) reported that the gelatinized starch could become retrograded after being kept at the optimal temperature of approximately 4 째C. It is possible that when the cooked rice was rinsed in cold water, the particles in the rice kernel that gelatinized during the cooking process may have begun to bond together again, creating a more cohesive structure. That could explain why the rice that was rinsed in cold water before freezing had a lower volume expansion rate

than rice that was not rinsed in cold water before freezing. Rehydration Ratio The rehydration ratios of all samples were different during rehydration for 2-40 min. The instant rice cooked in an electric rice cooker and frozen for 24 h (P2) had the highest water rehydration ratio while the instant rice that was cooked in an electric rice cooker, rinsed with cold water, and then frozen for 2 h before drying (P4) had the lowest water rehydration ratio. The water rehydration ratios of the instant rice products that were frozen for 24 h and cooked either by boiling (P1) or by using an electric rice cooker (P2) were very similar. The water rehydration ratios of these samples were higher than those of the samples that were rinsed with cold water and frozen for 2 h (Figure 3). 52

T. Limsuwan et al.

Silpakorn U Science & Tech J Vol.6(1), 2012

Figure 3 Rehydration ratio of instant rice one minute and increased throughout the duration of the testing period (Figure 4). The instant rice cooked by using an electric rice cooker and frozen for 24 hours before drying (P2) absorbed more water than other samples and its moisture content reached the same level of moisture as in the freshly cooked rice (65%) in 1.5 min. While the rehydration time to reach the same level of moisture content in freshly cooked rice for P1, P3 and P4 were 3, 3.5 and 3.5 min, respectively.

P1 = rice boiled + frozen for 24 h P2 = rice cooked in an electric rice cooker + frozen for 24 h P3 = rice boiled + rinsed + frozen for 2 h P4 = rice cooked in an electric rice cooker + rinsed + frozen for 2 h Rehydration Time All the instant rice samples showed their rehydration pattern in the similar manner. The moisture contents of all samples reached 50â&#x20AC;&#x201C;63% in

Figure 4 Rehydration times of instant rice

Silpakorn U Science & Tech J Vol.6(1), 2012

Development of Instant Rice for Young Children

boiling, frozen for 24 h prior to drying (P1), and rehydrated in boiling water for 3 min showed no statistically significant difference in L* (lightness) from freshly cooked rice. The other instant rice samples showed a statistically significant difference (p < 0.05) in L* (lightness) from the freshly cooked rice. As for the a* (redness) and b* (yellowness) values, P2, P3 and P4 showed significantly lower values (p < 0.05) than the freshly cooked rice (Table 1).

Table 1 Colour values of rehydrated instant rice compared to freshly cooked rice Method

Colour value L*

Freshly cooked rice

74.73 ± 0.11b

–1.86 ± 0.07a

5.03 ± 0.04b

Boiled–frozen (24 h)–dried (P1)

75.01 ± 0.20b

–2.03 ± 0.05c

5.63 ± 0.05a

Cooker–frozen (24 h)–dried (P2)

75.58 ± 0.15a

–1.98 ± 0.02b

4.12 ± 0.10c

Boiled–rinsed–frozen (2 h)–dried (P3)

72.10 ± 0.29c

–1.95 ± 0.03b

4.42 ± 0.06d

Cooker–rinsed–frozen (2 h)–dried (P4)

71.70 ± 0.19d

–1.96 ± 0.02b

4.80 ± 0.17c

Note: values are means ± standard deviation from three replications The different superscripts of values in the same column signify that the values differ to a statistically significant degree (P < 0.05).

Texture The texture of instant rice products after rehydrated by boiling at 3, 4 and 5 min were evaluated in order to find the suitable rehydration time. With regard to hardness, rice cooked by boiling showed significantly higher hardness values (p < 0.05) than rice cooked by the electric rice cooker (Table 2). A similar result was found by Rewthong et al. (2011). Tester and Morrison (1990) explained the difference in textural characteristics of cooked rice is probably related to the amount of leached starch during cooking. The longer cooking time resulted in a larger amount of leached starch (Chiang and Yeh, 2002). Therefore this could explain the higher hardness values for rice cooked by boiling

than rice cooked by the electric rice cooker since rice cooked by the electric rice cooker took longer time; 22 min versus 9 min for rice cooked by boiling. Similar result was observed with the hydration time. Instant rice products rehydrated at 5 min gave lower hardness values than instant rice products rehydrated at 3 and 4 min (Table 2). Rewthong et al. (2011) also suggested that rinsing rice with cold water prior to freezing helped to reduce leached starch during cooking. The samples that were rinsed in cold water prior to freezing (P3 and P4) were observed to have a significant higher hardness values (p < 0.05) than samples that were not rinsed before freezing (P1 and P2).

T. Limsuwan et al.

Silpakorn U Science & Tech J Vol.6(1), 2012

When compare to the freshly cooked rice only the instant rice product P1 showed no statistically

significant difference in hardness from the freshly cooked rice either rehydration at 3, 4 or 5 min.

Table 2 Hardness of rehydrated instant rice products compared to freshly cooked rice Hardness over boiling time (N)

Method

3 min

4 min

5 min

Freshly cooked rice

346.03 ± 7.64C,a

346.03 ± 7.64B,a

346.03 ± 7.64A,a

Boiled–frozen (24 h)–dried (P1)

349.75 ± 3.94C,a

345.97 ± 5.06B,a

330.93 ± 0.61AB,b

Cooker–frozen (24 h)–dried (P2)

310.27 ± 0.95D,a

306.20 ± 6.50C,a

275.93 ± 9.48C,b

Boiled–rinsed–frozen (2 h)–dried(P3)

454.62 ± 7.99A,a

419.03 ± 1.38A,b

344.54 ± 5.98A,c

Cooker–rinsed–frozen (2 h)–dried (P4)

376.46 ± 0.33B,a

342.58 ± 1.05B,b

314.35 ± 2.07B,c

Note: values are means ± standard deviation from five replications Different upper case superscripts in the same column signify that the values differ to a statistically significant degree (P < 0.05).

Different lower case superscripts in the same row signify that they differ to a statistically significant degree (P

< 0.05).

With regard to adhesiveness, the rice cooked by the electric rice cooker showed significantly higher values (p < 0.05) of adhesiveness than the rice cooked by the boiling method when rehydrated at 3 min (Table 3). This could be a result of the larger amount of leached starch when cooked longer time by the electric rice cooker (Chiang and Yeh, 2002). The adhesiveness tended to increase with rehydration time from 3 to 5 min, however, the significant difference was only found with the adhesiveness values of P1 and P2 when rehydrated at 3 minutes from 4 and 5 min and no significant

difference were found with the adhesiveness values of P3 and P4. The pre-rinsed samples with cold water before freezing tended to have lower values of adhesiveness than the no-rinsed samples. However, the significant differences (p < 0.05) were only found between P1 and P3 when rehydrated at 3, 4 and 5 min and between P2 and P4 when rehydrated at 4 min. The instant rice product whose adhesiveness was the most similar to that of freshly cooked rice (–21.25 ± 6.65 N.s) was the product prepared by the boiling method, frozen for 24 h, and rehydrated by boiling for 3 min (Table 3).

Silpakorn U Science & Tech J Vol.6(1), 2012

Development of Instant Rice for Young Children

Table 3 Adhesiveness of rehydrated instant rice compared to freshly cooked rice Adhesiveness over boiling time (N.s)

Method

3 min

4 min

5 min

Freshly cooked rice

–21.25 ± 6.65B,a

–21.25 ± 6.65AB,a

Boiled–frozen (24 h)–dried (P1)

–23.09 ± 1.30B,a

–53.80 ± 3.01E,b

–59.30 ± 8.26D,b

Cooker–frozen (24 h)–dried (P2)

–36.19 ± 1.27C,a

–45.34 ± 1.67D,b

–43.45 ± 2.90C,b

Boiled–rinsed–frozen (2 h)–dried (P3)

–12.74 ± 2.68A,a

–8.67 ± 0.90A,a

–8.50 ± 1.37A,a

Cooker–rinsed–frozen (2 h)–dried (P4)

–30.55 ± 4.80C,a

–33.29 ± 4.77C,a

–31.40 ± 5.45BC,a

Note: values are means ± standard deviation from five replications.

The minus sign indicates the values obtained from the area below the graph.

Different upper case superscripts in the same column signify that the values differ to a statistically significant

degree (P < 0.05).

Different lower case superscripts in the same row signify that the values differ to a statistically significant degree

(P < 0.05).

The cohesiveness data obtained from the tests showed that the instant rice samples produced by boiling method tended to have greater cohesiveness than the samples produced by using the electric rice cooker (P1>P2 and P3>P4) (Table 4). No major difference in cohesiveness was noted between samples of instant rice that were rinsed with cold water before freezing and those that were not.

All the instant rice samples except P3 had lower cohesiveness than the freshly cooked rice. The instant rice whose cohesiveness value was the most similar to that of freshly cooked rice (0.50±0.01) was the product that was prepared by the boiling method, frozen for 24 h (P1), and rehydrated by boiling for 3 or 4 min.

Table 4 Cohesiveness of rehydrated instant rice compared to freshly cooked rice Method

Cohesiveness over boiling time 3 min

4 min

5 min

Freshly cooked rice

0.50 ± 0.01

Boiled–frozen (24 h)–dried (P1)

0.49 ± 0.01B,a

0.48 ± 0.01A,ab

0.47 ± 0.01B,b

Cooker–frozen (24 h)–dried (P2)

0.48 ± 0.01B,a

0.45 ± 0.01B,b

0.45 ± 0.02C,b

Boiled–rinsed–frozen (2 h)–dried (P3)

0.58 ± 0.02A,a

<0.01 ± 0.00C,b

<0.01 ± 0.00D,b

Cooker–rinsed–frozen (2 h)–dried (P4)

0.01 ± 0.00C,a

0.01 ± 0.00D,a

B,a

A,a

0.50 ± 0.01

0.50 ± 0.01A,a

Note: values are means ± standard deviation from five repetitions.

Different upper case superscripts in the same column signify that the values differ to a statistically significant

degree (P < 0.05).

Different lower case superscripts in the same row signify that they differ to a statistically significant degree (P

< 0.05).

T. Limsuwan et al.

Silpakorn U Science & Tech J Vol.6(1), 2012

From the texture data above it can be concluded that the different methods of preparing instant rice have an effect on their texture when rehydrated. The texture is related to the amount of starch and the components of starch that are released from starch granules in the rice when it is heated (Rewthong et al., 2011). Ong and Blanshard (1995) reported that the amounts of amylose and short-chain amylopectin, major components of the leaching starch, affect the hardness and stickiness of cooked rice. The morphology of rice cooked by using an electric rice cooker showed more deformation of the porous structure at the external surface than the rice cooked by boiling, which indicates that more starch leached out during cooking (Rewthong et al., 2011). This could be due to the longer cooking time by the electric rice cooker (Chiang and Yeh, 2002) and could explain why P2 and P4 had lower hardness and cohesiveness but greater adhesiveness values than P1 and P3, respectively. When the cooked rice was rinsed with cold water before freezing, this may have reduced the amount of leaching starch (Rewthong et al., 2011), causing the instant rice samples that were rinsed before freezing and

drying to have greater hardness compared to freshly cooked rice. The results of texture analysis showed that the instant rice sample prepared by boiling and freezing gave no significant difference in hardness, adhesiveness, and cohesiveness values from the freshly cooked rice similar to the result of Rewthong et al. (2011). Sensory Evaluation When the samples were tested by 10 panelists who have experience in preparing food for infants and young children at the university child care center, the products that were boiled and frozen for 24 h before drying (P1 and P2) were given significantly higher liking scores (p < 0.05) for stickiness, softness, and overall acceptability than those that were pre-rinsed with cold water and frozen for only 2 h before drying (P3 and P4) except the overall acceptability for P4. The boiled-frozen for 24 h (P1) sample received the highest scores ranging between 7-8 from 9-point score (like moderately- like very much) for use as rice for young children (Table 5). The panelists also gave their acceptance when the product was mashed for preparing complemenry food for the infant.

Table 5 Sensory evaluations of rehydrated instant rice Method

Sensory evaluation scores Stickiness

Softness

Overall acceptability

Boiled–frozen (24 h)–dried (P1)

7.72 ± 0.79a

8.14 ±0.69a

7.86 ± 0.69a

Cooker–frozen (24 h)–dried (P2)

7.71 ± 0.76a

8.00 ± 0.82a

7.14 ± 1.07a

Boiled–rinsed–frozen (2 h)–dried (P3)

6.14 ± 1.10b

6.43 ± 0.98b

6.14 ± 0.69b

Cooker–rinsed–frozen (2 h)–dried (P4)

6.57 ± 0.98b

6.43 ± 0.98b

7.29 ± 0.95a

Note: values are means ± standard deviation from the scores given by 10 panelists.

Different superscripts in the same column signify that the values differ to a statistically significant degree (P <

0.05).

Silpakorn U Science & Tech J Vol.6(1), 2012

Development of Instant Rice for Young Children

Conclusion A comparison of methods for preparing instant rice products from Thai Jasmine rice for young children showed that the method of cooking and the method of pre-treatment before drying had an effect on the water rehydration ratio, volume expansion, rehydration time, and texture of the finished product when it was rehydrated. The instant rice prepared by boiling, pre-frozen for 24 h before drying, and then rehydrated by boiling for 3 min gave hardness, adhesiveness, and cohesiveness values that were not significantly different from those of freshly cooked rice. The sensory panelists also gave the highest scores for stickiness, softness, and overall acceptability. It is therefore recommended that boiling and 24 h freezing prior to drying is suitable to be used as a method for producing instant rice for young children.

Kongseree, N., Wongpiyachon, S., Sawangjit, P., Youngsuk, L., and Hirannupakorn, W. (2002) Production of instant rice. Research during 1991-2001. Department of Rice Research and Development, Ministry of Agriculture and Cooperatives (in Thai). Lu, T.-J., Jane, J.-L., and Keeling, P. L. (1997) Temperature effect on retrogradation rate and crystalline structure of amylose. Carbohydrate Polymers 33: 19-26. Luangmalawat, P., Prachayawarakorn, S., Nathakaranakule, A., and Soponronnarit, S. (2008) Effect of temperature on drying characteristics and quality of cooked rice. Journal of LWT 41: 716-723. Mohamed, A., Peterson, S. C., Grant, L. A., and Rayas-Duarte, P. (2006) Effect of jet-cooked wheat gluten/lecithin blends on maize and rice starch retrogradation. Journal of Cereal Science 43: 293â&#x20AC;&#x201C;300. Ong, M. H. and Blanshard, J. M. V. (1995) Texture determinants in cooked, parboiled rice: I. Rice starch amylose and the fine structure of amylopectin. Journal of Cereal Science 21: 251-260. Prasert, W. and Suwannaporn, P. (2009) Optimization of instant jasmine rice process and its physicochemical properties. Journal of Food Engineering 95: 54-61. Rewthong, O., Soponronnarit, S., Taechapairoj, C., Tungtrakul, P., and Prachayawarakorn, S. (2011) Effects of cooking, drying and pretreatment methods on texture and starch digestibility of instant rice. Journal of Food Engineering 103: 258-264. Tester, R. F. and Morrison, W. R. (1990) Swelling and gelatinization of cereal starches. Effects of amylopectin, amylase and lipids. Cereal Chemistry 67: 551-557.

Acknowledgements The authors would like to thank the National Research Council of Thailand for research funding. References AOAC. (2000). Official Methods of Analysis, 17th ed., Arlington. Carlson, R. A., Roberts, R. L., and Farkas, D. F. (1979) Process for preparing quick-cooking rice. U.S. Patent No. 4133,898. Chiang, P. Y. and Yeh, A. I. (2002) Effect of soaking on wet-milling of rice. Journal of Cereal Science 35: 85-94. Kiathanapaiboon, S. (2008) Relation among chemical, physical, and descriptive sensory qualities and likeness of different varieties of rice cooked by different methods. Thesis, Kasetsart University (in Thai).