Applications of the grey prediction model in Urban Residents' Consumption Structure of Henan Province

International Journal of Modern Research in Engineering & Management (IJMREM)
||Volume|| 1||Issue|| 7 ||Pages|| 07-14 || July 2018|| ISSN: 2581-4540
www.ijmrem.com IJMREM Page 7
 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
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Date of Submission: Date, 30 May 2018 Date of Accepted: 10 July 2018
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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-perspective, 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 residentsundefined 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 between

Applications of the grey prediction model in Urban Residents’…
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
Fig. 1 Line Chart of Per Capita Consumption Expenditure of Urban Rresidents in Henan Province
Index 2009 2010 2011 2012 2013 2014 2015 2016
Food 3272.8 3575.8 4212.8 4607.5 4913.9 5300.5 4818.7 5067.7
Clothes 1270.7 1444.6 1706.9 1886 1917 2058.6 1797.6 1394.4
Live 1004.4 1080.1 1087.1 1990.8 1315.3 1395 3391.1 3753.4
Household 684.8 866.7 977.5 1145.4 1281.1 1418.3 1382.2 1430.2
Medical Treatment 875.5 941.3 919.8 1085.5 1054.5 1117.5 1365.5 1524.5
Traffic 1034 1374.8 1573.6 1730.3 1768.3 1888.3 1874.1 1993.8
Entertainment 1048.1 1137.2 1373.9 1525.3 1911.2 2138.9 1991.9 2078.7
Others 376.7 418 484.8 562.1 660.8 692.3 533.1 845.1
Expenditure 9567 10838.5 12336.5 13733 14822 15726.1 17154.3 18087.8

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 patientsundefined 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 residentsundefined 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.

Fig. 3 Per Capita Cash Expenditure of Urban Residents in Henan Province
3.1 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
(0) (0) (0) (0)
( (1), (2), , ( ))X x x x n
where raw material
(0)
X stands for the non-negative original historical time series data.
Step 2: Construct
(1)
X by one time accumulated generating operation (1-AGO), which is
(1) (1) (1) (1)
( (1), (2), , ( ))X x x x n ,
where
(1) (0)
(1) (1)x x and (1) (0)
1
( ) ( )
k
i
x k x i

  , 1,2, ,k n .
Step 3: The GM(1,1) model can be constructed by establishing a first order differential equation for
(1)
( )x k as:
(1)
(1)( )
( )
dx k
ax k b
dk
  .
The solution of equation can be obtained by using the least square method. That is,
ˆ(1) (0) ( 1)
ˆ ˆ
ˆ ( ) (1)
ˆ ˆ
a kb b
x k x e
a a
 
 
     
 
, (1)
where
1ˆˆ[ , ] ( )T T T
na b B B B X
 , and
(1) (1)
(1) (1)
(1) (1)
0.5( (1) (2)) 1
0.5( (2) (3)) 1
... ...
0.5( ( 1) ( ) 1
x x
x x
x n x
B
n
  
 
  
 
 
  


,
(0) (0) (0) (0)
( (2), (3), (4), , ( ))T
nX x x x x n .
We obtained
(1)
ˆx from Eq. (1). Let
(0)
ˆx be the fitted and predicted series,
 (0) (0) (0) (0) (0)
ˆ ˆ ˆ ˆ ˆ(1), (2), (3), , ( ),x x x x x n ,
where
(0) (0)
ˆ (1) (1)x x , and applying the inverse AGO, we then have
ˆ ˆ(0) (0) ( 1)
ˆ
ˆ ( ) (1) (1 ) , 2,3, ,
ˆ
a a kb
x k x e e k
a
 
 
     
 
here
(0) (0) (0) (0)
ˆ ˆ ˆ ˆ(1), (2), (3), , ( )x x x x n are called the GM(1,1) fitted sequence, while
(0)
ˆ ( 1)x n  ,
(0)
ˆ ( 2),x n  , are called the GM(1,1) forecast values.

3.2 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:
(0) (0) (0) (0)
( (1), (2), , (8))
(9567,10838.5,12336.5,13733,14822,15726.1,17154.3,18087.8).
x x x x

Step 3: Calculate the grade ratio
0
0
( 1)
( )
( )
x k
k
x k


 .
0.883 0.879 0.89( (2), (3) 8 0.92, , (8) 7,0.943 0.917 . 8) 0 94     ( , , , , , ) .
Step 4: Judgment the grade ratio. If all grades ratio ( )k are within the allowable coverage
2 2
1 2
( , ) (0.879,0.948)n n
e e

 
 .
then the series can be used as the data of the model GM(1, 1) to forecast.
3.3 THE RESULTS AND ANALYSIS OF GM(1,1)
Step 1: Do an accumulation of the raw data
(0)
x .
5 T
1X 10 (0.096,0.204,0.327,0.465,0.613,0.770,0.942,1.123) . 
Step 2: Constructing the data B matrix and the data vector Y .
(1) (1)
(1) (1)
(1) (1)
0.5( (1) (2)) 1
0.5( (2) (3)) 1
... ...
0.5( ( 1) ( ) 1
x x
x x
x n x
B
n
  
 
  
 
 
  


,
4
(0)
(0)
(0)
1.084
1.234
1.482
10 *
1.57
(2)
(3)
...
(8
3
1.715
1
)
.809
x
Y
x
x
 
                    
 
.
Step 3: Calculating ˆu . According to the least square method, we can obtain that
1
ˆ ( , ) ( ) 1000*( 0.00017,1.016) ,T T T T
u a b B B B Y
   
and 0.00017, 1.016a b   . It can be seen that the value 0.00017a   is close to zero, which
shows that the grey forecasting model is suitable for the system.
Step 4: Constructing the model.
(1)
(1)
0.000117 5.113428
dx
x
dt
- = ,
the solution is
(1) (0) 0.000117
( 1) ( (1) ) 5294.2 51130 43865.355.ak kb b
x k x e e
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.

Table 3 Test Prediction Value
Year Actual value Predicted value
2009 9567.0 9567.0
2010 10838.5 11383.0
2011 12336.5 12334.0
2012 13733.0 13365.0
2013 14822.0 14482.0
2014 15726.1 15693.0
2015 17154.3 17004.0
2016 18087.8 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 Predictive Value
2017 19965
2018 21634
2019 23442
2020 25402
2021 27525
2022 29825
2023 32318
2024 35019
2025 37946
2026 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.

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:
1
( )
n
ji
k
ji
k
r
n
x
=
=
å
,
where n is the index number. jir 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.
4.1 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 jx and the comparison sequence
1 2, , , ix x x
:
min min ( ) ( ) max max ( ) ( )
( ) ,
( ) ( ) max max ( ) ( )
j i j i
ji
j i j i
x k x k x k x k
k
x k x k x k x k
r
x
r
- + -
=
- + -
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.
Table 4 Grey Correlation Degree of Per Capita Consumption Expenditure and Ranking Order
Index Food Clothes Live Household Medical Treatment Traffic Entertainment Others
Grey Correlation
Degree
0.859 0.813 0.628 0.734 0.690 0.789 0.844 0.814
Ranking order 1 4 8 6 7 5 2 3

4.2 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).
REFERENCES
Journal Papers:
[1] Shi Y. China’s consumption structure of urban residents empirical analysis of factors affecting. Capital
University of Economics and Business, 2010.
[2] Wang Y, Zhao Y. Urban residents' consumption structure analysis of He'nan Province. Journal of Anyang
Institute of Technology, 2015, 14(6): 90-93.
[3] Li H, Wu X, Zeng C. An empirical analysis of the upgrading trend of urban residents' consumption structure
in Henan under the new normal. Value Engineering, 2017, 36(8):22-23.
[4] Wang L, Zhang N. Comparative Analysis of Urban and Rural Residents’Consumption Structure in Henan
Province. Chinese Agricultural Science Bulletin, 2016, 32(1): 193-199.
[5] Guo H. On Consumption and Economic Growth Momentum in the 13th Five-Year Plan in Henan
Province[J]. Journal of North China University of Water Resources and Electric Power(Social Science
Edition), 2017, 33(1):52-55.
[6] Yu X, Xu Y. Analysis on consumption structure of Urban residents in Henan Province based on AIDS Model.
Business Economy, 2015(9):62-64.
[7] Feng Y, Guo W, ZHang J. Prediction and analysis impact factors on chongqing rural consumption
expenditure. Journal of Chongqing University of Technology(Social Science), 2012, 26(11): 40-46.
[8] Jiang J, Liang L. Study on per capita consumption of rural residents in Hunan Province based on grey
prediction method. Economic Research Guide, 2014 (9): 28-31.
[9] M Ozaki, Y. Adachi, Y. Iwahori, and N. Ishii, Application of fuzzy theory to writer recognition of Chinese
characters, International Journal of Modelling and Simulation, 18(2), 1998, 112-116.
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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