International Journal of Modern Research in Engineering & Management (IJMREM) ||Volume|| 1||Issue|| 7 ||Pages|| 07-14 || July 2018|| ISSN: 2581-4540
Applications of the grey prediction model in Urban Residents’ Consumption Structure of Henan Province Yong Wei Yang, Yang Yang He, Ming Xue Guo School of Mathematics and Statistics, Anyang Normal University, Anyang, China ---------------------------------------------------------ABSTRACT----------------------------------------------------------This paper first analyses the development trend of residents’ consumption Henan province from 2009 to 2016. Then the grey prediction model GM (1, 1) is applied to predict the change trend of residents’ consumption of Henan provinc. Finally, the paper puts forward some suggestions on the upgrading of the consumption structure of urban residents.
KEYWORDS: Urban residents, Consumption structure, Grey prediction model ----------------------------------------------------------------------------------------------------------------------------- --------Date of Submission: Date, 30 May 2018 Date of Accepted: 10 July 2018 ----------------------------------------------------------------------------------------------------------------------------- --------I. INTRODUCTION After China’s reform and opening up was implemented, the economic and political system reforms brought about rapid economic growth, which led to earth-shaking changes in the income levels and quality of life of urban residents. The consumption structure has also undergone significant changes. The consumption structure is one of the multi-perspectives, multi-level regulatory and operational economic scope can reflect the residents' consumption level, consumption quality, and consumption level, etc. [1]. Therefore, the study of urban residents' consumption and its changes will help to adjust the industrial structure and optimize resources. The allocation of economic growth and the formulation of various economic policies and plans are all of great significance. After the implementation of reform and opening up in China, the reform of economic and political system has brought about the rapid growth of economy, and the income level and quality of life of urban residents have also undergone earth-shaking changes, and their consumption structure has also changed significantly. The consumption structure is a multi-angle, multi-level and operable economic category, which can reflect the consumption level, consumption quality and consumption level of the residents [1]. Therefore, it is of great significance to study the consumption of urban residents and their changes for adjusting the industrial structure, optimizing the allocation of resources, stimulating economic growth and formulating various economic policies and plans [2]. Henan Province is a large populous province in China. According to the "Statistical Bulletin on the National economy and Development of Henan Province 2016" announced jointly by the Henan Province and the State Henan Survey Corps, it is known that at the end of 2016, the total population reaches 107.87 million and the urbanization rate is 48.5%. The per capita disposable income of the urban residents in the province is 27,232.92 yuan. It can be seen that the consumer groups in Henan Province are huge and there is a large consumption potential that can be tapped. According to the changes in the consumption structure research, different scholars will qualitatively study Henan residents undefined consumption from the aspects of research content and research methods. [3,4] used the extended linear expenditure (ELES) model in the empirical analysis of the urban urban residents' consumption structure in Henan, and obtained the change rule of residents' consumption structure and put forward some suggestions. Guo [5] studies the motive mechanism of consumption on Henan economic growth during the Thirteenth Five-Year Plan period from the perspective of basic function. Yu and Xu analyzed the consumption structure of urban residents in Henan Province by using the AID model, and obtained that the consumption of food, clothing and medical treatment by urban households in Henan will decline in the future. The consumption of transportation, communication and education, culture and entertainment will continue to increase [6]. However, the above study on the urban residents' consumption in Henan Province only obtained the consumption structure based on the existing data, but did not make reasonable predictions on the future consumption expenditures of Henan residents; in addition, the small sample data of research methods will affect the research results. The grey correlation analysis method can overcome these problems very well, and this method does not require a large amount of sample data, and can accurately measure the degree of correlation
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Applications of the grey prediction model in Urban Residents’… between systems [7]. With the improvement of urban residents' living standards, the consumption structure of the residents is constantly changing. It is helpful for the government to understand the changes of the consumption structure of the residents in time and accurately. This paper starts with the consumption structure, studies the internal structure of urban residents' household consumption in Henan Province, and analyzes the development trend and regularity of the consumption structure. Then the grey forecast model is used to predict the future trend of urban residentsundefined per capita consumption, and the grey correlation analysis method is used to determine the degree of correlation between the consumption expenditure and its statistical index factors, and the suggestions for optimizing the consumption structure of urban residents are put forward.
II. THE CURRENT SITUATION OF THE CONSUMPTION STRUCTURE OF URBAN RESIDENTS IN HENAN PROVINCE The changes in the consumption structure of residents are closely related to economic growth and the increase in income of residents. From the changes in the consumption structure, we can find out the development trend of residents' consumer demand and consumption structure. From Table 1 and Fig. 1, Fig. 2 can be seen that urban residents in Henan Province Consumption status: (1) Consumption of basic consumption is increasing steadily, but the proportion of food and clothing is decreasing gradually. In 2016, the per capita consumption expenditure on food, tobacco and wine was 18087.8 yuan, accounting for 28.0% of the total consumption of eight categories, an increase of 5.4% over the same period of last year and 1.89 times that of 9567 yuan in 2009. Per capita consumption of household goods and services is 1430.23 yuan, an increase of 3.5% over the same period of last year. Per capita spending on clothing rose from 1270.7 yuan in 2009 to 3753.4 yuan in 2016, and the proportion of consumption decreased from 34.21% in 2009 to 7.71% in 2016. However, the per capita consumption of food accounts for the share of urban households' consumer spending in 2016 decreased from 34.21% in 2009 to 28.02% in 2016. This shows that with the development of the province’s economy, the income of urban residents is increasing, and after the basic survival needs are met, people’s demand for information is increasing, and they are gradually moving from the stage of survival to development and enjoyment. Table 1 Per Capita Consumption Expenditure of Urban Residents in Henan Province, 2009-2016 Unit: Yuan Index
2009
2010
2011
2012
2013
2014
2015
2016
Food Clothes Live
3272.8 1270.7 1004.4
3575.8 1444.6 1080.1
4212.8 1706.9 1087.1
4607.5 1886 1990.8
4913.9 1917 1315.3
5300.5 2058.6 1395
4818.7 1797.6 3391.1
5067.7 1394.4 3753.4
Household
684.8
866.7
977.5
1145.4
1281.1
1418.3
1382.2
1430.2
Medical Treatment Traffic Entertainment Others
875.5 1034 1048.1 376.7
941.3 1374.8 1137.2 418
919.8 1573.6 1373.9 484.8
1085.5 1730.3 1525.3 562.1
1054.5 1768.3 1911.2 660.8
1117.5 1888.3 2138.9 692.3
1365.5 1874.1 1991.9 533.1
1524.5 1993.8 2078.7 845.1
Expenditure
9567
10838.5
12336.5
13733
14822
15726.1
17154.3
18087.8
6000 5000
food
4000
clothes
3000
live
2000
household
1000
medical treatment
0
traffic 2009 2010 2011 2012 2013 2014 2015 2016
Fig. 1 Line Chart of Per Capita Consumption Expenditure of Urban Residents in Henan Province
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Applications of the grey prediction model in Urban Residents’…
Proportion of per capita consumption expenditure of urban residents % 40.00 30.00 20.00 10.00 0.00
food clothes live household medical treatment
Fig. 2 Proportion of Per Capita Consumption Expenditure of Urban Residents in Henan Province (2) Residential consumption continues to increase. In recent years, the commercial reform of housing has intensified peopleundefineds spending on living. In 2016, the Henan real estate market was rapidly warming up and urban expansion was expanded, and the per capita living expenditure of urban residents in the province was 3753.4 yuan, which was 3.5 times the consumption expenditure in 2009, but the proportion in the consumption structure dropped by 2.59 percentage points, which show that the housing problem of urban residents in Henan Province has been partially solved. (3) The concept of medical consumption is gradually changing and the long-term consumption will increase accordingly. In health care, per capita spending jumped from 875.5 yuan in 2009 to 1524.5 yuan in 2016, an increase of nearly 2 times, while the proportion of consumer spending is a little change. In 2016, Henan Province realized the integration of medical insurance for urban and rural residents, solved the problem of difficulty in obtaining medical care in different places, and made the coverage of medical insurance continuously expand and the burden on patients undefined expenses continuously reduced. The concept of medical care and health of urban residents has gradually changed from "cure type" to "health type". In 2016, the per capita medical and health care expenditure of Henan residents was 1524.52 yuan, up 11.6 yuan from the same period of last year. (4) The consumption demand for traffic and communication is very strong. In 2016, the per capita expenditure on transportation and communications was 1993.8 yuan, an increase of 6.4 percent over the same period last year. The amount of expenditure increased from 1,034 yuan in 2009 to 1993.8 yuan in 2016, an increase of nearly 1 time. With the improvement of the convenience and comfort of transportation facilities and the increase of private car ownership, the choice of travel is increasing, and the increase of transportation consumption of urban residents is accelerated. In addition, the continuous increase in the quality of communication tools and networks has stimulated an increase in residents’ communications spending. (5) The consumption of education, culture and entertainment continues to increase. With the with the diversification of education and learning, as well as the diversification of entertainment forms, the per capita expenditure on education, culture and entertainment for urban residents was 2078.7 yuan in 2016, an increase of 4.4%. Urban residents undefined consumption of education and skills training after school for their children has not decreased, resulting in 1122.26-yuan per capita education expenditure in 2016, an increase of 18.7%. Through the above analysis we can see that the consumption structure of urban residents in Henan Province has been greatly improved.
III. GREY PREDICTION OF URBAN RESIDENTS' CONSUMPTION EXPENDITURE IN HENAN PROVINCE Gray prediction is a mathematical model proposed by Prof. Deng Julong in 1982 for a system that contains both known information and unknown information. Gray prediction can predict the gray process related to time series that changes within a certain range. The most widely used grey prediction model GM (1, 1) is based on a random original time series. The law of the new time series formed after the accumulation by time can be approximated by the solution of a first order linear differential equation [7] . Fig. 3 shows that during the eight years from 2009 to 2016, per capita consumption expenditure of urban households in Henan Province showed an increasing trend, which was roughly positively correlated. According to this trend of consumer spending, we can use the grey model GM (1, 1) for the future. The forecast of per capita consumption of urban residents for 10 years.
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Applications of the grey prediction model in Urban Residents’… 20000 15000 10000
9567
10838.5
12336.5
13733
14822 15726.1
18087.8 17154.3
5000 0 2009
2010
2011
2012
2013
2014
2015
2016
Fig. 3 Per Capita Cash Expenditure of Urban Residents in Henan Province
THE MATHEMATICAL MODEL OF GM (1,1) : In Grey theory, the accumulated generating operation (AGO) technique is applied to reduce the randomization of the raw data. These processed data become monotonic increase sequence which complies with the solution of first order linear ordinary differential equation. Therefore, the solution curve would fit to the raw data with high precision. In the following section, the derivation of GM (1,1) is briefly described: Step 1: Assume that the original series of data with m entries is
X (0) ( x(0) (1), x(0) (2), , x(0) (n)) (0) where raw material X stands for the non-negative original historical time series data. (1) Step 2: Construct X by one-time accumulated generating operation (1-AGO), which is X (1) ( x(1) (1), x(1) (2), , x(1) (n)) , where x (1) x (1)
k
(0)
(1) and x (1) (k ) x (0) (i) , k 1, 2,
,n.
i 1
Step 3: The GM (1,1) model can be constructed by establishing a first order differential equation for (1)
x (k ) as:
dx (1) (k ) ax (1) (k ) b . dk The solution of equation can be obtained by using the least square method. That is,
bˆ bˆ xˆ (1) (k ) x (0) (1) e aˆ ( k 1) , aˆ aˆ
(1)
0.5( x (1) (1) x (1) (2)) 1 (1) (1) 0.5( x (2) x (3)) 1 T T 1 T ˆ where [aˆ, b] ( B B) B X n , and B , ... ... (1) (1) 0.5( x (n 1) x (n) 1 X n ( x(0) (2), x(0) (3), x(0) (4), , x(0) (n))T .
x̂ (1) from Eq. (1). Let x̂ (0) be the fitted and predicted series, xˆ (0) (1), xˆ (0) (2), xˆ (0) (3), , xˆ (0) (n), ,
We obtained
xˆ (0)
(1) x(0) (1) , and applying the inverse AGO, we then have bˆ xˆ (0) (k ) x (0) (1) (1 eaˆ )e aˆ ( k 1) , k 2,3, , aˆ (0) (0) (0) (0) (0) here xˆ (1), xˆ (2), xˆ (3), , xˆ (n) are called the GM(1,1) fitted sequence, while xˆ (n 1) , where xˆ
xˆ (0) (n 2),
(0)
, are called the GM(1,1) forecast values.
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Applications of the grey prediction model in Urban Residents’… Verification of Data Columns Step 1: Extraction of per capita consumption expenditure data: Table 2 Per Capita Consumption Expenditure of Urban Households No.
1
2
3
4
5
6
7
8
Year
2009
2010
2011
2012
2013
2014
2015
2016
Expenditure (yuan)
9567
10838.5
12336.5
13733
14822
15726.1
17154.3
18087.8
Step 2: Grade test. Establishment of a time series of data on human settlements consumption expenditures:
x(0) ( x(0) (1), x(0) (2),
, x(0) (8))
(9567,10838.5,12336.5,13733,14822,15726.1,17154.3,18087.8). x 0 (k 1) . x 0 (k ) ( (2), (3), , (8)) ( 0.883,0.879,0.898,0.927,0.943,0.917,0.948) . Step 4: Judgment the grade ratio. If all grades ratio (k ) are within the allowable coverage Step 3: Calculate the grade ratio
(e
2 n 1
,e
2 n2
(k )
) (0.879, 0.948) .
then the series can be used as the data of the model GM (1, 1) to forecast. The Results and Analysis of GM (1,1) Step 1: Do an accumulation of the raw data
x (0) .
X1 105 (0.096,0.204,0.327,0.465,0.613,0.770, 0.942,1.123)T . Step 2: Constructing the data B matrix and the data vector Y . 1.084 1.234 (1) (1) (0) 0.5( x (1) x (2)) x (2) 1 (0) (1) (1) 1.482 0.5( x (2) x (3)) 1 x (3) , Y 104 * B . ... 1.573 ... ... (0) (1) (1) 1.715 0.5( x (n 1) x (n) 1 x (8) 1.809 Step 3: Calculating û . According to the least square method, we can obtain that
uˆ (a, b)T ( BT B)1 BT Y 1000*(0.00017,1.016)T , and a 0.00017, b 1.016 . It can be seen that the value a 0.00017 is close to zero, which shows that the grey forecasting model is suitable for the system. Step 4: Constructing the model.
dx(1) - 0.000117 x (1) = 5.113428 , dt the solution is
b b x(1) (k 1) ( x(0) (1) )e ak 5294.2e0.000117 k 51130 43865.355. a a
Step 5: Model testing. From Table 3, it can be seen that the actual value and the predicted value are not much different. In fig. 4, the residuals (the difference between the observed value and the predicted value) and the error show that the confidence interval passes through the origin, which shows that the equation fits well. It can be seen from the relative error diagram that the data error of per capita cash consumption expenditure in cities and towns from 2009-2016 to 2016 is less than 5%, which shows that the prediction of the model is good.
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Applications of the grey prediction model in Urban Residents’… Table 3 Test Prediction Value Year
Actual value
Predicted value
2009
9567.0
9567.0
2010
10838.5
11383.0
2011 2012 2013
12336.5 13733.0 14822.0
12334.0 13365.0 14482.0
2014 2015 2016
15726.1 17154.3 18087.8
15693.0 17004.0 18425.0
Fig. 4 Residuals and Errors of Per Capita Consumption Expenditure
Step 6: Results. This paper forecasts the per capita cash consumption of urban residents in Henan Province in 2017-2026 by using the GM (1, 1) model. The forecast results are shown in Table 4 and Fig. 5. Table 4 Predictive Value of Current Consumer Expenditure Per Capita in the Next 10 Years Year 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026
Predictive Value 19965 21634 23442 25402 27525 29825 32318 35019 37946 41118
It can be seen from Fig. 5 that the forecast value of per capita cash consumption expenditure of urban residents in Henan Province in 2017-2026 shows a linear upward trend, indicating that urban residents’ living standards are getting higher and higher, and consumption demand is becoming higher and higher.
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Applications of the grey prediction model in Urban Residents’…
Fig. 5 Actual and Forecasted Cash Expenditure
IV. GREY RELATIONAL ANALYSIS OF PER CAPITA CONSUMPTION EXPENDITURE OF URBAN RESIDENTS IN HENAN PROVINCE The method of grey correlation analysis [7,8] is a method to judge the correlation degree between factors according to the degree of similarity or dissimilarity among factors, that is, "grey correlation degree". Correlation coefficient refers to the degree of relevance of each point in the curve described by the comparison of each factor index sequence and the corresponding reference sequence between the object to be recognized and the value of the influencing factors. However, due to the diversification of the object, it presents a number of values that make it difficult to compare them as a whole. Therefore, we need to calculate the average correlation coefficient of each point as the correlation degree between the comparison series of various factors and their corresponding reference series, where the correlation between them is: n
rji = where
åx
ji
k =1
n
(k ) ,
n is the index number? rji is closer to 1, indicating that the stronger the correlation is, the greater than
0.7 is called a strong correlation, and the less than 0.3 is called a weak correlation. Calculation and Steps of Grey Correlation Degree: Step 1: Determine the reference sequence and the comparison sequence. Here, the reference sequence is a data sequence that reflects the characteristics of the system's behavior, and the sequence of comparisons is a sequence of data that influences the behavior of the system. Step 2: Calculate the gray correlation coefficient of the above reference sequence and comparison sequence. The correlation coefficient between the reference sequence x j and the comparison sequence
x1 , x2 ,
, xi
:
x ji (k ) =
min min x j (k ) - xi (k ) + r max max x j (k ) - xi (k ) x j (k ) - xi (k ) + r max max x j (k ) - xi (k )
where is the resolution coefficient, the value between 0
,
1, we often take 0.5?
Step 3: Selection ranking. The degree of correlation between factors is mainly described by the order of magnitude of the correlation degree. The correlation degree between the sub-sequence and the same parent sequence is sorted according to the size, and then the association order is formed, which reflects the "good and bad" relation of each sub-sequence relative to the parent sequence. Here, we choose the per capita consumer expenditure as the reference series and the eight-factor index as the comparison series. The calculation results are shown in Table 5.
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Applications of the grey prediction model in Urban Residents’… Table 4 Grey Correlation Degree of Per Capita Consumption Expenditure and Ranking Order
Index Grey Correlation Degree Ranking order
Food
Clothes
Live
Household Medical Treatment
Traffic Entertainment Others
0.859
0.813
0.628
0.734
0.690
0.789
0.844
0.814
1
4
8
6
7
5
2
3
Conclusions and Suggestions: From 2009 to 2016, the consumption structure of urban residents in Henan Province has gradually become more rationalized. With the improvement of the living standards of residents, the proportion of urban residents in food consumption has decreased, while the other proportion has shown an upward trend, but in health care, education and entertainment, the increase is not very obvious. Residents in Henan Province should reduce consumer spending in traditional areas and switch to other new consumption areas. However, as the consumption structure is affected by many factors, it is a good way to optimize the consumption structure of urban residents to improve the income level and the consumption confidence of the residents. With the rapid growth of new consumer kinetic energy in China and the gradual improvement of consumer policy measures, Henan Province should closely follow the relevant national policies, straighten out the income distribution relationship of the residents of the province, speed up the industrial structure, and improve the income distribution system. While adjusting and raising residents’ income, we should narrow the income gap of residents and reform the commodity circulation system, actively improve the consumption environment, and expand residents’ consumption.
ACKNOWLEDGEMENTS The works described in this paper are partially supported by Undergraduate Innovation Foundation Project of Anyang Normal University (No. ASCX/2018-Z112) and the 2017 Teaching Research Project of Anyang Normal University (No. ASJY-YB-047).
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Yong Wei Yang. “Applications of the Grey Prediction Model in Urban Residents’ Consumption Structure of Henan Province.” International Journal of Modern Research in Engineering & Management (IJMREM), vol. 1, no. 7, 6 July 2018, ijmrem.com.
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