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

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.


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.

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 3. The absolute difference sequences Δ 0 ( ) between reference sequence 0 ( ) and comparison sequences ( ) are calculated by the formula (2) Step 4. Identify the absolute maximum Δ max and minimum Δ min from absolute difference sequence.
Step 5. Calculate the grey relational coefficient. The formula is Step 6. Calculate correlation degree.

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]: In the formula, 1 , 2 , and 3 are the undetermined parameters (regression parameters), with for unobservable random error.

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 is the predictive value in time of various influence factors and −1 , −2 , . . . , − are actual values of various impact factors in past years. Setting = (1 − ) , among it, is a single integer sequence with order; is the stationary series [11]; thus the general model of the ARMA model can be expressed as In the formula, and are, respectively, called autoregressive order number and average order number. Suppose as the lag operator; then Equation (6) can be rewritten as Among it, ( ) = 1 − 1 − 2 2 − ⋅ ⋅ ⋅ − and Θ( ) = 1 + 1 + 2 2 + ⋅ ⋅ ⋅ + . ARMA( , ) model in formula (7) can be expressed as ARIMA( , , ) after order difference transformation is a white noise process with its mean value which is 0 and variance is 2 [12].

Simulation Analysis
The dynamic simulation process based on the ARIMA model and multiple regression model to predict feed grain demand is shown in Figure 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 from Rural 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]. 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 Table 1 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.
As shown in Table 2, 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.

Impact Factors Prediction
. ARIMA( , , ) 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.

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: Among them, 0 and 1 represent the urban and rural feed grain demand, respectively, 01 is urban population, and 11 is rural population. 02 and 12 represent urbanization level, 03 is urban residents per capita income, and 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.

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.
From Table 4 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.

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, 4 Computational Intelligence and Neuroscience