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Research & Reviews : Journal of Statistics

Contents

1. Examining market efficiency of Chittagong Stock Exchange (CSE) in Bangladesh: An Empirical Analysis of the Random Walk Hypothesis H.M. Simon, Md. Siddikur Rahman

2. Review Script on Vedic Arithmetic Multiplication Kapil Babbar

3. Revenue Forecasting using Holtâ&#x20AC;&#x201C;Winters Exponential Smoothing Md. Habibur Rahman, Umma Salma, Md. Moyazzem Hossain, Md. Tareq Ferdous Khan

4. Comparison Study on the Prediction Performance of Different Statistical Models including Feed Forward Artificial Neural Network: Climate Data of Some Coastal Districts Md. Habibur Rahman

5. Analysis of Earthquake Risk Influencing Factors by Using Logistic Regression Model of RC Frame Buildings Nanda Kumar Tharu, Ram Prasad Khatiwada

Research & Reviews: Journal of Statistics ISSN: 2278-2273(online), ISSN: 2348-7909(print) Volume 5, Issue 3 www.stmjournals.com

Examining Market Efficiency of Chittagong Stock Exchange (CSE) in Bangladesh: An Empirical Analysis of the Random Walk Hypothesis H.M. Simon, Md. Siddikur Rahman* Department of Statistics, Begum Rokeya University, Rangpur, Bangladesh Abstract Hypothesis of market efficiency is an important concept for the investors who wish to hold internationally diversified portfolios. With increased movement of investments across international boundaries owing to the integration of world economies, the understanding of efficiency of the emerging markets is also gaining greater importance. In this paper, we test the weak form efficiency in the framework of random walk hypothesis for Chittagong stock exchange (CSE) by composing daily returns of three indices for the period of 2006 to 2015. The evidence suggests that the series do not follow random walk model and there is an evidence applying different tests of rejecting the weak form efficiency hypothesis. Keywords: Market efficiency, random walk hypothesis, Jarque-Bera test, CSE

INTRODUCTION During the past decades stock market sees as an engine of a strong and modern economy in developing countries considering that it is a more progressive financial system than a traditional rigid, insecure bank based financial system. The stock market in developing countries like Bangladesh achieves more intentness to apportion the necessary capital demand for the stolid of their economy. Through all kinds of subsistence instability the stock market of Bangladesh keeps growing and continuously contributes to our economy. The Chittagong stock exchange (CSE) has come to our concern and subject of this paper of market efficiency [1–4]. In Bangladesh the Chittagong stock exchange plays a central and significant role in economic sector. From then, economist and financial researchers devoted their work to find the efficiency of the stock market. However, the ability of a stock market is depending on the information, operational and allocational efficiency (Lagoardesegot and Lucey, 2008) [5]. According to Fama (1970) [6] a market is efficient when the stock prices should follow a random walk and the price movements in the past should be not related to

future price movements, if market is not efficient it follows the opposite site of the random walk theory .

LITERATURE REVIEW A major focus of empirical finance literature has centered on the accomplishment of financial markets and their efficiency to shareout investment capital within economy. In many growth strategists, access to investment capital, mainly through well terminating financial markets, is decisive for economic development (Obstfeld. 1994) [7]. In recent years consequently we have seen on increasing notability of stock markets in developing regions of the world like Bangladesh. Over the past thirty years hundreds of studies have been tested on the “Efficient Market Hypothesis”, starting form [8, 9] [Fama and French (1996), McQueen, Pinegar, and Thorley (1996), Malkiel (1995), Brown and Goetzmann(1995), Ikenberry, Lakonishok, and Vermaelen (1995), Elton, Gruber, Das, and Hlavka (1993), Goetzmann and Ibbotson (1994), Jegadeesh, and Titman (1993), Chopra, Lakonishok, and Ritter (1992), Seppi (1992), Lee, Shleifer, and Thaler (1991), Bernard and Thomas (1990, 1989), Harris (1989), Ippolito (1989), Ball and Kothari (1989), DeBondt and Thaler (1989,

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Research & Reviews: Journal of Statistics ISSN: 2278-2273(online), ISSN: 2348-7909(print) Volume 5, Issue 3 www.stmjournals.com

Review Script on Vedic Arithmetic Multiplication Kapil Babbar* Department of Mechanical, Tantia University, Sri Ganganagar, Rajasthan, India Abstract Multiplication is an important fundamental function in arithmetic operations. Arithmetical multiplications of numbers are carried out more simply and faster using Vedic mathematics sutras and subsutras. In this script, we study about four Vedic mathematic sutras and three Vedic mathematics subsutras. In this, all sutras and subsutras are illustrated by means of examples. This study shows that in all cases the time taken by the sutras or subsutras for mathematical operations do not exceed by the time taken in the conventional methods. A number of comments are given to the end of each problem. Keywords: Arithmetic, Vedic Mathematics

HISTORY Shri Bharti Krsna Tirthaji constitutes an original and unique system of mathematics using sutra and forms a new category of Vedic mathematics [1]. He rediscovered Vedic mathematics from the Vedas between 1911 and 1918. According to his research, Vedic mathematics was based on 16 sutras and 16 subsutras [2]. These sutras or subsutras are easy to understand, easy to apply and easy to remember [2]. Vedic mathematics has important feature that is its coherence which is most striking and it simply means in Vedic mathematics whole system is beautifully interrelated and unified instead of a hotchpotch. Vedic mathematics provides a different and simple kind of approach for solving a large variety of problems. All difficult or huge type of problems can be easily solved immediately in Vedic mathematics. In this, the whole work can be truthfully summarised in one word ‘Mental’. It means that calculations are carried out mentally and it is the simplicity of the Vedic mathematics. Interest in Vedic mathematics is growing in education. The mathematics teachers are looking for something better in Vedic system. Various researches are carried out in many areas some as:  The effect of learning Vedic maths on children.



Developing new, powerful but easy applications of Vedic sutras in different fields.

But the real beauty and effectiveness of Vedic mathematics cannot be fully appreciated without actually practicing the system. It is may be the most refined and efficient mathematical system possible [3].

MULTIPLICATION OF NUMBERS For performing the arithmetical calculation of multiplications, Vedic Mathematics provides four sutras: 1. Ekadhiken Purven 2. Ekanyunen Purvena 3. Urdhva Triyagbhyam 4. Nikhilam Method Vedic Mathematics also provides two subsutras, which are studied under sutra Ekadhiken Purven: 1. Ekadhiken Purven 1.1 Yavdunam Tavdunikritya Vargamch Yojaget 1.2 Antyayor Deshkepi All the methods of multiplication are explained below one by one. Ekadhiken Purven This sutra means “By one more than previous one”. It is the first Vedic sutra. It is applied for finding the square of a number that is end with five. As this manuscript is on multiplication

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Research & Reviews: Journal of Statistics ISSN: 2278-2273(online), ISSN: 2348-7909(print) Volume 5, Issue 3 www.stmjournals.com

Revenue Forecasting using Holt–Winters Exponential Smoothing Md. Habibur Rahman1,*, Umma Salma2, Md. Moyazzem Hossain3, Md. Tareq Ferdous Khan4 1,3,4 2

Department of Statistics, Jahangirnagar University, Dhaka, Bangladesh Research Evaluation Associates for Development Ltd., Dhaka, Bangladesh

Abstract A lot of time series demonstrate seasonal behavior with trend, such type of series was monthly revenue (in crore) of Bangabandhu Multipurpose Bridge. The seasonal forecasting with trend issue was considerable importance. The research work focus on the analysis of seasonal time series data using additive and multiplicative seasonal model of Holt–winters method and forecast the monthly revenue (in crore) using best model—additive Holt–Winters exponential smoothing up to January 2021. Keywords: Forecast, levels, seasonality, trend, root mean squared, Bangladesh

INTRODUCTION Forecasting was most often part of a larger process of planning and managing, and a forecast was necessary to provide accurate estimates of the future for the larger process. The all of forecasting methods were classified under the types—time series univariate methods, causal or multivariate methods, qualitative or technological, and other quantitative methods. The Holt–Winters method is a statistical forecasting method in time series univariate methods. The forecasting engages make projection about future performance on the basis of past and recent data. Dasgupta SS, Mahanta P, Roy R, Subramanian G. (2014) [1] forecast industry big data with Holt–Winters method. Exponential smoothing models and auto regressive moving average model compared to comprehend which method is more adapted to model the temperature behavior in Caserta, Italy (Guizzi G, Silvestri C, Romano E, Revetria R, 2015) [2]. Taylor JW (2003) [3] applied the Holt– Winters method to forecast short-term electricity demand. Holt (2004) [4] extended the exponential weighed moving averages to allow trend and seasonal variation. Holt– Winters exponential smoothing is a popular approach to forecasting seasonal time series. Winters method and Fourier series analysis are versatile methods because the methods model

the level, trend, and seasonality of a time series (DeLurgio SA, 1998) [5]. Puah YJ, Huang YF, Chua KC, Lee TS. (2016) [6] were modeled the Rainfall series using additive Holt–Winters method to examine the rainfall pattern in Langat River Basin, Malaysia. The Holt–Winters exponential smoothing is one of the most popular methods to forecast the different time series. The main objective of the research work was fit the additive Holt– Winters exponential smoothing model, check the accuracy measures, and forecast the monthly revenue (in crore) of the Bangabandhu multipurpose bridge.

DATA DESCRIPTION The monthly revenue (in crore) from July 1998 to July 2016 was plotted and shown in Figure 1. The mean revenue found to be 16.917 with standard deviation 8.9375. The quantile—quantile plot and box plot was presented in the Figure 2. The monthly revenue data normally distributed. From the above time series plot, it was evident that the seasonality and trend was present in the series. The seasonal length of the series was twelve (Table 1).

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Research & Reviews: Journal of Statistics ISSN: 2278-2273(online), ISSN: 2348-7909(print) Volume 5, Issue 3 www.stmjournals.com

Comparison Study on the Prediction Performance of Different Statistical Models including Feed Forward Artificial Neural Network: Climate Data of Some Coastal Districts Md. Habibur Rahman* Department of Statistics, Jahangirnagar University, Dhaka, Bangladesh

Abstract This study compares the performance of different statistical models and artificial neural network models in predicting the monthly average rainfall in monsoon season and over the year. The data used in this study is collected from the Bangladesh Meteorological Department consisting 18 stations for the year 1961â&#x20AC;&#x201C;2014. The prediction performance of models are evaluated by different accuracy measures such as mean absolute deviation, mean absolute percentage error, root mean square error, prediction error, similarity measures, Akaike information criterion, Schwarz information criterion, etc. It reveals that the different seasonal average rainfall and yearly average rainfall is approximately normally distributed and the variability of monsoon rainfall is superior to the other seasons. In predicting both the series, several models such as linear trend, single exponential smoothing, double exponential smoothing, Fourier series, polynomial, auto regressive integrated moving average, multiple linear regression, artificial neural network model are employed. According to model accuracy measure, the best fitted models are Fourier series and polynomial. Keywords: Rainfall, artificial neural network, statistical model, model accuracy measure, prediction performance

INTRODUCTION Bangladesh is a natural disaster prone country and every year the country struck by several catastrophic natural disasters such as drought, flood, cyclone, storm, erosion etc. Rainfall may work as significant factor resulting several disasters more especially flood due to excess rainfall and drought because of lack of rainfall. In Bangladesh, rainfall level varies over the year. In monsoon, the level is high sometimes which causes flood and on the other hand, the level is very low, especially in pre-monsoon season results drought in some areas of the country. Therefore, getting the idea about the rainfall may help a lot in policy making decision. Several models have been using in predicting rainfall in different countries. Sohn et al. (2005) [1] used linear regression, logistic regression, neural network, and decision tree models for forecasting the occurrence of heavy rainfall in South Korea. The multiple linear

regression was used by Rajeevan et al. (2007) [2] to forecast the south west monsoon rainfall over India. Sadhuram and Murthy (2008) [3] also predicted Indian summer monsoon rainfall by a linear multiple regression model. In 2012, Afshar and Fahmi [4] applied Fourier series model to forecast the monthly rainfall of Iran. The additive Holt-Winters method applied to analyze the monthly and seasonal rainfall series of Langat River Basin in Malaysia (Puah et al. 2016) [5]. The exponential smoothing model and auto regressive integrated moving average model have been compared to comprehend which method is more adapted to model the temperature behavior of Caserta in Italy (Guizzi et al., 2015) [6]. Singhrattna et al. (2005) [7] developed the statistical forecasting methodâ&#x20AC;&#x201D;linear regression and local polynomial-based nonparametric for summer monsoon rainfall in Thailand. In Caribbean, Ashby et al. (2005) [8] used the statistical

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Research & Reviews: Journal of Statistics ISSN: 2278-2273(online), ISSN: 2348-7909(print) Volume 5, Issue 3 www.stmjournals.com

Analysis of Earthquake Risk Influencing Factors by Using Logistic Regression Model of RC Frame Buildings Nanda Kumar Tharu*, Ram Prasad Khatiwada Central Department of Statistics, Tribhuvan University, Kirtipur, Kathmandu, Nepal Abstract This article categorizes and statistically presents various risk influencing factors on damages of homes and buildings during ‘Nepal Earthquake 2015’ in a hilly municipality Chautara of Sindhupalchok District, Nepal. This work analyses risk factors with different measures and presents a statistical model on damage patterns (livable/not-livable) of Reinforced Concrete (RC) frame buildings of the study area using logistic regression model. Proposed model is validated with Forward Stepwise Selection (FSS) and Backward Stepwise Selection (BSS), using R2 (Hosmer and Lameshow, Cox and Snell, Negelkerke) and Chi-square tests. Model adequacy test is done with multicollinearity test, goodness of fit and residual plots and ensured into satisfactory result. The predicted probabilities of the risk for not-livable damages of the buildings are also computed for various ages and storeys. Keywords: Earthquake risk, RC frame buildings, logistic regression, maximum likelihood, multicollinearity, variance inflation factor

INTRODUCTION An earthquake is a geological event inside the earth that generates strong vibrations. When the vibrations reach the surface, the earth shakes, often causing damage to natural and manmade objects, and sometimes killing and injuring people and destroying their property. Earthquakes can occur for a variety of reasons; however, the most common source of earthquake is movement along a fault [1]. The 25 April 2015, Nepal Earthquake also known as the Gorkha Earthquake which killed over 9,000 people and injured more than 23,000. It occurred at 11:56 Nepal Standard Time (NST) on 25 April, with a magnitude of 7.8 Mw. Its epicenter was east of the district of Lamjung, and its hypocenter was at a depth of approximately 8.2 km. It was the most horrible natural disaster to strike Nepal since the 1934 Nepal-Bihar earthquake [2]. Hundreds of thousands of people were made homeless with entire villages flattened, across many districts of the country. Centuries-old buildings were destroyed at

UNESCO world heritage sites in the Kathmandu valley, including some at the Kathmandu Durbar Square, the Patan Durbar Square, the Bhaktapur Durbar Square, the Changu Narayan Temple and the Swayambhunath Stupa. Geophysicists and other experts had warned for decades that Nepal was vulnerable to a deadly earthquake, particularly because of its geology, urbanization, and architecture [3]. Shaking Intensity Profile The modified Mercalli Intensity (MMI) scale depicts shaking severity. The area nearest Katmandu experienced very strong to severe shaking (Figure 1). Introduction of Study Area Chautara municipality is a municipality in Sindhupalchowk district in the Bagmati zone of central Nepal. It is the only settlement in the Sindhupalchowk district with the administrative status of municipality. The municipality was established in 18 May 2014 merging Pipaldanda, Chautara, Kubhinde, and Sanusiruwari VDC. This is the district headquarters of the Sindhupalchowk district (Figure 2).

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