# A Forecasting Model for Feed Grain Demand Based on Combined Dynamic Model

Authors: Tiejun Yang; Na Yang; Chunhua Zhu
Journal: Computational Intelligence and Neuroscience
 (2016)

---

## Abstract

In order to improve the long-term prediction accuracy of feed grain demand, a dynamic forecast model of long-term feed grain demand is realized with joint multivariate regression model, of which the correlation between the feed grain demand and its influence factors is analyzed firstly; then the change trend of various factors that affect the feed grain demand is predicted by using ARIMA model. The simulation results show that the accuracy of proposed combined dynamic forecasting model is obviously higher than that of the grey system model. Thus, it indicates that the proposed algorithm is effective.


---

## Body

## 1. Introduction

The grain used in feeding is the second largest grain used in China; its quantity and proportion of the total grain consumption grow stably. It is of great significance to ensure food security in our country by exploring the changes of feed grain demand and its influencing factors. However, the special research of China’s feed grain demand is scattered, which lacks objective statistics and always exists in projections of the total grain consumption. The forecasting methods of feed grain demand in existing literature can be divided into two kinds: one is using some quantitative methods such as time series regression, model of consumer demand system, and farming grain consumption, based on the analysis about the situation of the feeding food consumption over the past few years to analysis and forecast [1, 2]; the other is from the perspective of nutrition standards analysis of meat, eggs, milk, per capita consumption of aquatic products to predict the future demand for animal products and then use the ratio of feed to meat (i.e., the conversion rate of feed grains) to predict the feed grain demand [3, 4]. Actually, the feed grain demand is affected by population growth, urbanization level, per capita income (urban residents per capita income and rural ones per capita income), and other factors [5, 6], which suggest that there should be a comprehensive survey about correlation degree between the feed grain demand and its influence factors for improving the prediction accuracy, and the corresponding prediction model should be generalized. In this paper, the correlation coefficients of feed grain demand and its influence factors are calculated quantitatively on the basis of the second kind of forecasting method; then the major factors have been chosen; finally the dynamic prediction of influence factors and feed grain demand can be realized by using the ARIMA model and multiple regression model, respectively.


## 2. Relational Coefficient Analysis of Influence Factors to Feed Grain Demand

### 2.1. Grey Relational Analysis

The essence of grey relational degree is to make a geometric comparison in the data series which are responded to the changing characteristics of all factors. The closer the curves are, the greater the relational grade of the corresponding series is and vice versa. The use of the grey relational analysis can define the changing trend of all factors in this system and find out the main factors which affect the further development of the system so as to grasp the main features of things and the principal contradiction, promote, and guide the system to rapid, health, and efficient development [7]. The basic steps of grey relational analysis are as follows.Step 1.
Assume that the reference sequence isx
0
(
k
) and related comparison sequences are x
i
(
k
). They are expressed as x
0
(
k
)
=
{
x
0
(
1
)
,
x
0
(
2
)
,
…
,
x
0
(
n
)
} and(1)
x
i
k
=
x
i
1
,
x
i
2
,
…
,
x
i
n
,
i
=
1,2
,
…
,
m
.Step 2.
Dis-dimension treatment to the data sequence [8]. Here, we illustrate the initiating. Then it can get the reference sequence y
0
(
k
) and comparison sequences y
i
(
k
)
(
i
=
1,2
,
…
,
m
;
k
=
1,2
,
…
,
n
).Step 3.
The absolute difference sequencesΔ
0
i
k between reference sequence y
0
(
k
) and comparison sequences y
i
(
k
) are calculated by the formula(2)
Δ
0
i
k
=
y
0
k
-
y
i
k
=
Δ
i
1
,
Δ
i
2
,
…
,
Δ
i
n
,
i
=
1,2
,
…
,
m
.Step 4.
Identify the absolute maximumΔ
m
a
x and minimum Δ
m
i
n from absolute difference sequence.Step 5.
Calculate the grey relational coefficient. The formula is(3)
L
0
i
k
=
Δ
m
a
x
+
Δ
m
i
n
Δ
0
i
k
+
Δ
m
a
x
.Step 6.
Calculate correlation degree.(4)
R
0
i
k
=
1
n
∑
k
=
1
n
L
0
i
k
=
1
n
L
0
i
1
+
L
0
i
2
+
⋯
+
L
0
i
n
.


### 2.2. Prediction for the Feed Grain Demand by Using Multiple Linear Regression

According to grey relational analysis, the domestic population, urbanization level, and per capita income of urban and rural residents are the main factors affecting the feed grain demand. Based on the modeling principle of multiple regression model, the linear regression model of the feed grain demand is set up, the structure form of the model [9]:(5)
y
0
=
U
0
+
U
1
x
1
+
U
2
x
2
+
U
3
x
3
+
ε
,
ε
~
N
0
,
δ
2
.In the formula,U
1, U
2, and U
3 are the undetermined parameters (regression parameters), with ε for unobservable random error.


### 2.3. Prediction for Main Factors That Influence the Feed Grain Demand

The ARIMA model from literature is adopted to predict the change trend of impact factors [10]. Suppose that ω
t is the predictive value in t time of various influence factors and ω
t
-
1
,
ω
t
-
2
,
…
,
ω
t
-
p are actual values of various impact factors in past p years. Setting ω
t
=
(
1
-
L
)
d
y
t, among it, y
t is a single integer sequence with d order; ω
t is the stationary series [11]; thus the general model of the ARMA model can be expressed as(6)
ω
t
=
φ
1
ω
t
-
1
+
φ
2
ω
t
-
2
+
⋯
+
φ
p
ω
t
-
p
+
ε
t
+
θ
1
ε
t
-
1
+
⋯
+
θ
q
ε
t
-
q
.In the formula,p and q are, respectively, called autoregressive order number and average order number. Suppose L as the lag operator; then(7)
L
ω
t
=
ω
t
-
1
,
L
p
ω
t
=
ω
t
-
p
.Equation (6) can be rewritten as (8)
φ
L
ω
t
=
Θ
L
ε
t
.Among it, φ
(
L
)
=
1
-
φ
1
L
-
φ
2
L
2
-
⋯
-
φ
p
L
p and Θ
(
L
)
=
1
+
θ
1
L
+
θ
2
L
2
+
⋯
+
θ
q
L
q.A
R
M
A
(
p
,
q
) model in formula (7) can be expressed as A
R
I
M
A
(
p
,
d
,
q
) after d order difference transformation(9)
φ
L
1
-
L
d
y
t
=
Θ
L
ε
t
.
ε
t is a white noise process with its mean value which is 0 and variance is σ
2 [12].


## 2.1. Grey Relational Analysis

The essence of grey relational degree is to make a geometric comparison in the data series which are responded to the changing characteristics of all factors. The closer the curves are, the greater the relational grade of the corresponding series is and vice versa. The use of the grey relational analysis can define the changing trend of all factors in this system and find out the main factors which affect the further development of the system so as to grasp the main features of things and the principal contradiction, promote, and guide the system to rapid, health, and efficient development [7]. The basic steps of grey relational analysis are as follows.Step 1.
Assume that the reference sequence isx
0
(
k
) and related comparison sequences are x
i
(
k
). They are expressed as x
0
(
k
)
=
{
x
0
(
1
)
,
x
0
(
2
)
,
…
,
x
0
(
n
)
} and(1)
x
i
k
=
x
i
1
,
x
i
2
,
…
,
x
i
n
,
i
=
1,2
,
…
,
m
.Step 2.
Dis-dimension treatment to the data sequence [8]. Here, we illustrate the initiating. Then it can get the reference sequence y
0
(
k
) and comparison sequences y
i
(
k
)
(
i
=
1,2
,
…
,
m
;
k
=
1,2
,
…
,
n
).Step 3.
The absolute difference sequencesΔ
0
i
k between reference sequence y
0
(
k
) and comparison sequences y
i
(
k
) are calculated by the formula(2)
Δ
0
i
k
=
y
0
k
-
y
i
k
=
Δ
i
1
,
Δ
i
2
,
…
,
Δ
i
n
,
i
=
1,2
,
…
,
m
.Step 4.
Identify the absolute maximumΔ
m
a
x and minimum Δ
m
i
n from absolute difference sequence.Step 5.
Calculate the grey relational coefficient. The formula is(3)
L
0
i
k
=
Δ
m
a
x
+
Δ
m
i
n
Δ
0
i
k
+
Δ
m
a
x
.Step 6.
Calculate correlation degree.(4)
R
0
i
k
=
1
n
∑
k
=
1
n
L
0
i
k
=
1
n
L
0
i
1
+
L
0
i
2
+
⋯
+
L
0
i
n
.


## 2.2. Prediction for the Feed Grain Demand by Using Multiple Linear Regression

According to grey relational analysis, the domestic population, urbanization level, and per capita income of urban and rural residents are the main factors affecting the feed grain demand. Based on the modeling principle of multiple regression model, the linear regression model of the feed grain demand is set up, the structure form of the model [9]:(5)
y
0
=
U
0
+
U
1
x
1
+
U
2
x
2
+
U
3
x
3
+
ε
,
ε
~
N
0
,
δ
2
.In the formula,U
1, U
2, and U
3 are the undetermined parameters (regression parameters), with ε for unobservable random error.


## 2.3. Prediction for Main Factors That Influence the Feed Grain Demand

The ARIMA model from literature is adopted to predict the change trend of impact factors [10]. Suppose that ω
t is the predictive value in t time of various influence factors and ω
t
-
1
,
ω
t
-
2
,
…
,
ω
t
-
p are actual values of various impact factors in past p years. Setting ω
t
=
(
1
-
L
)
d
y
t, among it, y
t is a single integer sequence with d order; ω
t is the stationary series [11]; thus the general model of the ARMA model can be expressed as(6)
ω
t
=
φ
1
ω
t
-
1
+
φ
2
ω
t
-
2
+
⋯
+
φ
p
ω
t
-
p
+
ε
t
+
θ
1
ε
t
-
1
+
⋯
+
θ
q
ε
t
-
q
.In the formula,p and q are, respectively, called autoregressive order number and average order number. Suppose L as the lag operator; then(7)
L
ω
t
=
ω
t
-
1
,
L
p
ω
t
=
ω
t
-
p
.Equation (6) can be rewritten as (8)
φ
L
ω
t
=
Θ
L
ε
t
.Among it, φ
(
L
)
=
1
-
φ
1
L
-
φ
2
L
2
-
⋯
-
φ
p
L
p and Θ
(
L
)
=
1
+
θ
1
L
+
θ
2
L
2
+
⋯
+
θ
q
L
q.A
R
M
A
(
p
,
q
) model in formula (7) can be expressed as A
R
I
M
A
(
p
,
d
,
q
) after d order difference transformation(9)
φ
L
1
-
L
d
y
t
=
Θ
L
ε
t
.
ε
t is a white noise process with its mean value which is 0 and variance is σ
2 [12].


## 3. Simulation Analysis

The dynamic simulation process based on the ARIMA model and multiple regression model to predict feed grain demand is shown in Figure1.Figure 1
Dynamic prediction simulation process of feed grain demand.The dynamic prediction algorithm of feed grain demand is shown in Figure1; define the year of 1981 as t
=
1 and thus 2007 as t
=
27. The feed grain demand of urban and rural population is, respectively, expressed as y
0
(
t
) and y
1
(
t
); the three factors are, respectively, defined as x
1
(
t
), x
2
(
t
), and x
3
(
t
). According to the simulation process shown in Figure 1, the forecast process of feed grain demand in this paper is shown in the following:(1)
Whent = 1~27, calculate the correlation degree and relational sequence, respectively, between y
0
(
t
) and y
1
(
t
) and x
1
(
t
), x
2
(
t
), and x
3
(
t
).
(2)
Use ARIMA model to predictx
1
(
t
), x
2
(
t
), and x
3
(
t
) when t
>
27.
(3)
Use multiple regression method to predict urban feed grain demandy
0
(
t
) (t
=
28) and rural feed grain demand y
1
(
t
) (t
=
28).
(4)
Repeat (3). Urban and rural long-term prediction of feed grain demand can be completed.


### 3.1. Correlation Calculation

The data about the feed grain demand, urban and rural population, urbanization level, and urban and rural residents per capita income between 1981 and 2007 are selected fromRural China Statistical Yearbook [13] as the training data; meanwhile the data from 2008 to 2012 are selected as the precision test data as shown in Table 1. The feed grain demand can be got by the sum of per capita meat, egg, milk, and aquatic product consumption multiplied by the urban and rural population, respectively, and then according to the conversion ratio of feed grain to meat which is 3.7 to 1, the conversion ratio to egg which is 2.7 to 1, the conversion ratio to milk which is 0.5 to 1, and the conversion ratio to aquatic material which is 0.4 to 1 to get the final result [14, 15].Table 1
Statistical data of various impact factors.
Year
Meat
Egg
Milk
Aquatic product
Population (ten thousand people)
Per capita income (yuan)
Urbanization level (%)
Urban
Rural
Urban
Rural
Urban
Rural
Urban
Rural
Urban
Rural
Urban
Rural
1981
20.5
9.4
5.2
1.3
4.1
0.7
7.3
1.3
20171
79901
500.4
223.4
14.2
1982
21
9.9
5.9
1.4
4.5
0.7
7.7
1.3
21480
80174
535.3
270.1
14.4
1983
22.5
10.8
6.9
1.6
4.6
0.8
8.1
1.6
22274
80734
564.6
309.8
14.6
1984
22.8
11.5
7.6
1.8
5.2
0.8
7.8
1.7
24017
80340
652.1
355.3
14.7
1985
24
12
8.8
2.1
6.4
0.8
7.8
1.6
25094
80757
739.1
397.6
14.8
1986
25.3
12.9
7.1
2.1
4.7
1.4
8.2
1.9
26366
81141
900.9
423.8
15
1987
25.4
12.9
6.6
2.3
5.5
1.1
7.9
2
27674
81626
1002.1
462.6
15.1
1988
23.7
12
6.9
2.3
5.1
1.1
7.1
1.9
28661
82365
1180.2
544.9
15.3
1989
23.9
12.3
7.1
2.4
4.2
1
7.6
2.1
29540
83164
1373.9
601.5
15.4
1990
25.2
12.6
7.3
2.4
4.6
1.1
7.7
2.1
30195
84138
1510.2
686.3
15.5
1991
26.6
13.5
8.3
2.7
4.7
1.3
8
2.2
31203
84620
1700.6
708.6
15.9
1992
26.5
13.3
9.5
2.9
5.5
1.5
8.2
2.3
32175
84996
2026.6
784
16.2
1993
26
13.3
8.9
2.9
5.4
0.9
8
2.8
33173
85344
2577.4
921.6
16.5
1994
24.3
12.6
9.7
3
5.3
0.7
8.5
3
34169
85681
3496.2
1221
16.8
1995
23.6
13.1
9.7
3.2
4.6
0.6
9.2
3.4
35174
85947
4283
1577.7
17.2
1996
25.8
14.8
9.6
3.4
4.8
0.8
9.25
3.7
37304
85085
4838.9
1926.1
18.4
1997
25.5
15.1
11.1
4.1
5.1
1
9.3
3.8
39449
84177
5160.3
2090.1
19.6
1998
25.5
15.5
10.2
4.1
6.2
0.9
9.84
3.7
41608
83153
5425.1
2162
20.8
1999
26.7
16.4
10.9
4.3
7.9
1
10.3
3.8
43748
82038
5854
2210.3
22
2000
25.4
18.3
11.2
4.8
9.9
1.1
11.7
3.9
45906
80837
6280
2253.4
23.2
2001
26.5
18.2
10.4
4.7
11.9
1.2
10.33
4.1
48064
79563
6859.6
2366.4
24.4
2002
32.5
18.6
10.6
4.7
15.7
1.2
13.2
4.4
50212
78241
7702.8
2475.6
25.8
2003
32.9
19.7
11.2
4.8
18.6
1.7
13.4
4.7
52376
76851
8472.2
2622.2
27.2
2004
29.3
19.2
10.4
4.6
18.8
2
12.5
4.5
54283
75705
9421.6
2936.4
28.9
2005
32.9
22.4
10.4
4.7
17.9
2.9
12.6
4.9
56212
74544
10493
3254.9
30.7
2006
32.1
22.3
10.4
5
18.3
3.1
13
5
58288
73160
11759.5
3587
32.5
2007
31.8
20.5
10.3
4.7
17.8
3.5
14.2
5.4
60633
71496
13785.8
4140.4
34.3
2008
31.2
20.2
10.7
5.4
15.2
3.4
11.9
5.2
62403
70399
15780.8
4760.6
36
2009
34.7
21.5
10.6
5.3
14.9
3.6
12.2
5.3
64512
68938
17174.7
5153.2
37.7
2010
34.7
22.2
10
5.1
14
3.6
15.2
5.2
66978
67113
19109.4
5919
38.8
2011
35.2
23.3
10.1
5.4
13.7
5.2
14.6
5.4
69079
65656
21809.8
6977.3
40.6
2012
35.7
23.5
10.5
5.9
14
5.3
15.2
5.4
71182
64222
24564.7
7916.6
42.4
Note: (1) unit: per capita consumption in kilograms; (2) the data are from Rural China Statistical Yearbook.The correlation degree and relational order are obtained by using the grey correlation analysis method, while the data about the feed grain demand are calculated in Table1 as reference sequence; at the same time urban and rural population, urbanization level, and urban and rural residents per capita income are calculated as comparative sequence. The results are shown in Table 2.Table 2
The grey correlation analysis about each influencing factor in 1981–2007 of urban and rural feed grain demand.
Influencing factor
Urban
Rural
Correlation degree
Relational order
Correlation degree
Relational order
(Urban/rural) population
0.9370
1
0.9255
2
Urbanization level
0.9047
2
0.9641
1
(Urban/rural) per capita income
0.7236
3
0.6881
3As shown in Table2, the correlation degree and relational order of various factors which affected the urban and rural feed grain demand are not completely the same; on the basis of that, it will be able to improve the prediction accuracy by predicting towns and rural feed grain demand separately.


### 3.2. Impact Factors Prediction

ARIMA(p
,
d
,
q) model described in Section 2.3 is adopted to predict the three factors including urban and rural population, urbanization level, and urban and rural residents per capita income. The prediction of impact factors for urban feed grain demand in 2008 is taken as an example in this paper, and the results are shown in Table 3. The forecast data will be used to forecast feed grain demand in 2008.Table 3
Predicted value of various influencing factors in 2008.
Influencing factor
Model
AdjustedR
2
Predicted value in 2008
Urban population
ARIMA(3, 2, 6)
0.956
62965.45
Urbanization level
ARIMA(7, 2, 2)
0.848
36.1254
Urban residents per capita income
ARIMA(4, 2, 5)
0.876
15872.19


### 3.3. Prediction for Feed Grain Demand by Using Multiple Regression

The multiple regression model of urban and rural demand for feed grain demands is set up, respectively, in 2008 by using EVIEWS statistical software, while three factors mentioned above are taken as independent variables and China’s urban and rural residents’ feed grain demand is taken as the dependent variable. The models are shown as follows:(10)
y
0
=
-
4240163
+
151.53
x
01
+
210419.4
x
02
-
195.0006
x
03
,
(11)
y
1
=
-
21283643
+
232.867
x
11
+
392070.5
x
12
-
543.328
x
13
.Among them,y
0 and y
1 represent the urban and rural feed grain demand, respectively, x
01 is urban population, and x
11 is rural population. x
02 and x
12 represent urbanization level, x
03 is urban residents per capita income, and x
13 is rural residents per capita income. The predicted value of three factors in 2008 was typed in (10) and (11), respectively; then the value of urban and rural feed grain demand in 2008 can be calculated; the results are 9807134 tons and 6663724.9 tons.In the above multivariate regression model of urban and rural feed grain demand, the model prediction coefficient of different years will change dynamically as the change of correlation of feed grains and affecting factors; then it forms a dynamic forecast system.


### 3.4. Simulation Results

The value of feed grain demand in 2008–2012 can be predicted according to (10) and (11); the result is shown in Table 4. A grey forecasting model by using residual error correction on the feed grain demand in literature [16] is also given in Table 4.Table 4
The comparison between the actual value and predicted value of feed grain demand under different prediction models (unit: ten thousand tons).
Year
Actual value
Predicted value
Relative error
Mean relative error
Combined dynamic forecasting model
2008
16332.1
16470.9
0.8%
0.46%
2009
17665.2
17795.3
0.7%
2010
17981.0
17928.4
0.2%
2011
18687.2
18798.5
0.5%
2012
19267.6
19243.8
0.1%
Grey forecasting model
2008
16332.1
17925.4
9.7%
6.4%
2009
17665.2
18426.9
4.3%
2010
17981.0
19246.7
7.0%
2011
18687.2
19875.1
6.4%
2012
19267.6
20144.8
4.6%From Table4 and combined with the feed grain demand between urban and rural areas since 1981, it can be seen that the basic trend of feed grain demand overall present rises steadily [17, 18]. The feed grain demand increased by 4 times, and the average annual growth rate is 14.8% from 1981 to 2007. Analysis shows that the income level of our country residents is low, and the consumption structure is unitary, mainly grain consumption before the reform and open policy. In recent years, the demand for animal products structure is changing and it mainly displays in the increasing demand for meat, eggs, milk, and aquatic products because people’s living standards have been continuously improved.In addition, compared with the grey system model in literature [16], the joint dynamic prediction model in this paper can track the change of impact factors, so it can achieve good long-term forecasts. Meanwhile the mean relative error of proposed model is 0.46% and has higher superiority in forecasting precision compared with traditional grey forecasting model of which the mean relative error is 6.4%. It is fully illustrated that the dynamic impact factor regression analysis method used to predict the feed grain demand is feasible.


## 3.1. Correlation Calculation

The data about the feed grain demand, urban and rural population, urbanization level, and urban and rural residents per capita income between 1981 and 2007 are selected fromRural China Statistical Yearbook [13] as the training data; meanwhile the data from 2008 to 2012 are selected as the precision test data as shown in Table 1. The feed grain demand can be got by the sum of per capita meat, egg, milk, and aquatic product consumption multiplied by the urban and rural population, respectively, and then according to the conversion ratio of feed grain to meat which is 3.7 to 1, the conversion ratio to egg which is 2.7 to 1, the conversion ratio to milk which is 0.5 to 1, and the conversion ratio to aquatic material which is 0.4 to 1 to get the final result [14, 15].Table 1
Statistical data of various impact factors.
Year
Meat
Egg
Milk
Aquatic product
Population (ten thousand people)
Per capita income (yuan)
Urbanization level (%)
Urban
Rural
Urban
Rural
Urban
Rural
Urban
Rural
Urban
Rural
Urban
Rural
1981
20.5
9.4
5.2
1.3
4.1
0.7
7.3
1.3
20171
79901
500.4
223.4
14.2
1982
21
9.9
5.9
1.4
4.5
0.7
7.7
1.3
21480
80174
535.3
270.1
14.4
1983
22.5
10.8
6.9
1.6
4.6
0.8
8.1
1.6
22274
80734
564.6
309.8
14.6
1984
22.8
11.5
7.6
1.8
5.2
0.8
7.8
1.7
24017
80340
652.1
355.3
14.7
1985
24
12
8.8
2.1
6.4
0.8
7.8
1.6
25094
80757
739.1
397.6
14.8
1986
25.3
12.9
7.1
2.1
4.7
1.4
8.2
1.9
26366
81141
900.9
423.8
15
1987
25.4
12.9
6.6
2.3
5.5
1.1
7.9
2
27674
81626
1002.1
462.6
15.1
1988
23.7
12
6.9
2.3
5.1
1.1
7.1
1.9
28661
82365
1180.2
544.9
15.3
1989
23.9
12.3
7.1
2.4
4.2
1
7.6
2.1
29540
83164
1373.9
601.5
15.4
1990
25.2
12.6
7.3
2.4
4.6
1.1
7.7
2.1
30195
84138
1510.2
686.3
15.5
1991
26.6
13.5
8.3
2.7
4.7
1.3
8
2.2
31203
84620
1700.6
708.6
15.9
1992
26.5
13.3
9.5
2.9
5.5
1.5
8.2
2.3
32175
84996
2026.6
784
16.2
1993
26
13.3
8.9
2.9
5.4
0.9
8
2.8
33173
85344
2577.4
921.6
16.5
1994
24.3
12.6
9.7
3
5.3
0.7
8.5
3
34169
85681
3496.2
1221
16.8
1995
23.6
13.1
9.7
3.2
4.6
0.6
9.2
3.4
35174
85947
4283
1577.7
17.2
1996
25.8
14.8
9.6
3.4
4.8
0.8
9.25
3.7
37304
85085
4838.9
1926.1
18.4
1997
25.5
15.1
11.1
4.1
5.1
1
9.3
3.8
39449
84177
5160.3
2090.1
19.6
1998
25.5
15.5
10.2
4.1
6.2
0.9
9.84
3.7
41608
83153
5425.1
2162
20.8
1999
26.7
16.4
10.9
4.3
7.9
1
10.3
3.8
43748
82038
5854
2210.3
22
2000
25.4
18.3
11.2
4.8
9.9
1.1
11.7
3.9
45906
80837
6280
2253.4
23.2
2001
26.5
18.2
10.4
4.7
11.9
1.2
10.33
4.1
48064
79563
6859.6
2366.4
24.4
2002
32.5
18.6
10.6
4.7
15.7
1.2
13.2
4.4
50212
78241
7702.8
2475.6
25.8
2003
32.9
19.7
11.2
4.8
18.6
1.7
13.4
4.7
52376
76851
8472.2
2622.2
27.2
2004
29.3
19.2
10.4
4.6
18.8
2
12.5
4.5
54283
75705
9421.6
2936.4
28.9
2005
32.9
22.4
10.4
4.7
17.9
2.9
12.6
4.9
56212
74544
10493
3254.9
30.7
2006
32.1
22.3
10.4
5
18.3
3.1
13
5
58288
73160
11759.5
3587
32.5
2007
31.8
20.5
10.3
4.7
17.8
3.5
14.2
5.4
60633
71496
13785.8
4140.4
34.3
2008
31.2
20.2
10.7
5.4
15.2
3.4
11.9
5.2
62403
70399
15780.8
4760.6
36
2009
34.7
21.5
10.6
5.3
14.9
3.6
12.2
5.3
64512
68938
17174.7
5153.2
37.7
2010
34.7
22.2
10
5.1
14
3.6
15.2
5.2
66978
67113
19109.4
5919
38.8
2011
35.2
23.3
10.1
5.4
13.7
5.2
14.6
5.4
69079
65656
21809.8
6977.3
40.6
2012
35.7
23.5
10.5
5.9
14
5.3
15.2
5.4
71182
64222
24564.7
7916.6
42.4
Note: (1) unit: per capita consumption in kilograms; (2) the data are from Rural China Statistical Yearbook.The correlation degree and relational order are obtained by using the grey correlation analysis method, while the data about the feed grain demand are calculated in Table1 as reference sequence; at the same time urban and rural population, urbanization level, and urban and rural residents per capita income are calculated as comparative sequence. The results are shown in Table 2.Table 2
The grey correlation analysis about each influencing factor in 1981–2007 of urban and rural feed grain demand.
Influencing factor
Urban
Rural
Correlation degree
Relational order
Correlation degree
Relational order
(Urban/rural) population
0.9370
1
0.9255
2
Urbanization level
0.9047
2
0.9641
1
(Urban/rural) per capita income
0.7236
3
0.6881
3As shown in Table2, the correlation degree and relational order of various factors which affected the urban and rural feed grain demand are not completely the same; on the basis of that, it will be able to improve the prediction accuracy by predicting towns and rural feed grain demand separately.


## 3.2. Impact Factors Prediction

ARIMA(p
,
d
,
q) model described in Section 2.3 is adopted to predict the three factors including urban and rural population, urbanization level, and urban and rural residents per capita income. The prediction of impact factors for urban feed grain demand in 2008 is taken as an example in this paper, and the results are shown in Table 3. The forecast data will be used to forecast feed grain demand in 2008.Table 3
Predicted value of various influencing factors in 2008.
Influencing factor
Model
AdjustedR
2
Predicted value in 2008
Urban population
ARIMA(3, 2, 6)
0.956
62965.45
Urbanization level
ARIMA(7, 2, 2)
0.848
36.1254
Urban residents per capita income
ARIMA(4, 2, 5)
0.876
15872.19


## 3.3. Prediction for Feed Grain Demand by Using Multiple Regression

The multiple regression model of urban and rural demand for feed grain demands is set up, respectively, in 2008 by using EVIEWS statistical software, while three factors mentioned above are taken as independent variables and China’s urban and rural residents’ feed grain demand is taken as the dependent variable. The models are shown as follows:(10)
y
0
=
-
4240163
+
151.53
x
01
+
210419.4
x
02
-
195.0006
x
03
,
(11)
y
1
=
-
21283643
+
232.867
x
11
+
392070.5
x
12
-
543.328
x
13
.Among them,y
0 and y
1 represent the urban and rural feed grain demand, respectively, x
01 is urban population, and x
11 is rural population. x
02 and x
12 represent urbanization level, x
03 is urban residents per capita income, and x
13 is rural residents per capita income. The predicted value of three factors in 2008 was typed in (10) and (11), respectively; then the value of urban and rural feed grain demand in 2008 can be calculated; the results are 9807134 tons and 6663724.9 tons.In the above multivariate regression model of urban and rural feed grain demand, the model prediction coefficient of different years will change dynamically as the change of correlation of feed grains and affecting factors; then it forms a dynamic forecast system.


## 3.4. Simulation Results

The value of feed grain demand in 2008–2012 can be predicted according to (10) and (11); the result is shown in Table 4. A grey forecasting model by using residual error correction on the feed grain demand in literature [16] is also given in Table 4.Table 4
The comparison between the actual value and predicted value of feed grain demand under different prediction models (unit: ten thousand tons).
Year
Actual value
Predicted value
Relative error
Mean relative error
Combined dynamic forecasting model
2008
16332.1
16470.9
0.8%
0.46%
2009
17665.2
17795.3
0.7%
2010
17981.0
17928.4
0.2%
2011
18687.2
18798.5
0.5%
2012
19267.6
19243.8
0.1%
Grey forecasting model
2008
16332.1
17925.4
9.7%
6.4%
2009
17665.2
18426.9
4.3%
2010
17981.0
19246.7
7.0%
2011
18687.2
19875.1
6.4%
2012
19267.6
20144.8
4.6%From Table4 and combined with the feed grain demand between urban and rural areas since 1981, it can be seen that the basic trend of feed grain demand overall present rises steadily [17, 18]. The feed grain demand increased by 4 times, and the average annual growth rate is 14.8% from 1981 to 2007. Analysis shows that the income level of our country residents is low, and the consumption structure is unitary, mainly grain consumption before the reform and open policy. In recent years, the demand for animal products structure is changing and it mainly displays in the increasing demand for meat, eggs, milk, and aquatic products because people’s living standards have been continuously improved.In addition, compared with the grey system model in literature [16], the joint dynamic prediction model in this paper can track the change of impact factors, so it can achieve good long-term forecasts. Meanwhile the mean relative error of proposed model is 0.46% and has higher superiority in forecasting precision compared with traditional grey forecasting model of which the mean relative error is 6.4%. It is fully illustrated that the dynamic impact factor regression analysis method used to predict the feed grain demand is feasible.


## 4. Conclusion

The dynamic influence factors in combination with multivariate regression analysis method are used in this paper to forecast the feed grain demand in China since 2008. Prediction results show that China’s demand for feed grains will increase year by year in the next 10 years, and the average relative error between the actual and predicted value by using the dynamic impact factor regression model is 0.46%, superior to the traditional grey system model. At present, China’s feed grain demand represents more than 30% of the total demand for grain; the proportion of which feed grain demand on total demand for grain increased year by year shows the increasing influence of feed grains on food security, so it has become a necessary work to research the feed grain demand deeply for ensuring food security.



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*Source: 5329870-2016-09-06.xml*