Application Study on the Prediction of Grain Output in Huainan by Grey GM ( 1 , 1 ) Model

In order to predict the future annual grain production in Huainan scientifically and accurately, according to the monotone increasing characteristics of the grain output in Huainan from 1995-2010, in this study, we predict the grain output from 2011 to 2014 by using the grey GM (1, 1) model and compare the prediction results with the real value, we find that the prediction has a good effect and the errors are within the scope of the permission. It is very significant for Huainan municipal government to make the corresponding economic development program, to preserve the social stability and to boost the living standards in Huainan.


INTRODUCTION
Agriculture is the foundation of the national economy.Food security is not only a basic question of influencing human survival and development (Chen and Zhang, 2005), but also a major strategic issue relating to national economic development and social stability.Therefore, it is very significant for the government to make the corresponding economic development program, to preserve the social stability and to boost the living standards through scientific and accurate prediction of the future annual grain production in some area.At present, the domestic researches on grain yield prediction mainly use BP (Wang, 2002) neural network, rough set theory (Yin, 2008) and multiple linear regression (Zhou et al., 2011), etc.Since Grey system theory proposed by Chinese well-known scholar Professor (Deng, 1987), it has been widely used in the economic, military, transportation, environmental fields and so on, especially the grey forecasting theory which regards the research object as a changeable function with the time.When modeling, without a lot of original data, we still can obtain a more accurate prediction results which has high precision (Xie et al., 2013).Huainan, stretching across the Huaihe River, is located in the north-central part of Anhui Province.In the history, food production is unstable because of the suffering of the drought and flood disaster.With the development of economy and technology, as well as the state constantly increasing inputs of the water conservancy project, the food production of Huainan increased year by year and the social economy has developed rapidly in recent years.In order to predict scientifically and accurately the future annual grain production in Huainan, in this study, we predict the grain output of Huainan by using the grey GM (1, 1) model and compare the prediction results with the real value, so that we can get the corresponding conclusions.

THE GREY GM (1, 1) MODEL
The general form of the grey prediction model: Set y (0) = {y (0) (i), i = 1, 2, … M} as the original data of an index to be predicted, gray prediction model is established by the following steps.
Step 3: We can obtain the predictive value of ˳ (1) (x) of linear accumulated generating sequences by the formula of ( 4) and then the reduced value of the original data is: And the provisions of ˳ (0) (0) = 0.

Test of the prediction accuracy of grey forecasting model:
The residual error ε (0) (k) and the relative error q (k) between predicted values of grey GM (1, 1) model and the real value can be calculated by using the formula of: In addition, we can test the prediction accuracy of formula (4) according to the following steps.
Step 1: Calculate: Step 2: Calculate the variance ratio of c = s 2 /s 1 and small error probability of: Step 3: Compare the result of calculation of step 2 with the numerical value of the prediction precision of test table (Table 1).For p value and c value not allowed within the scope, we should analyze the residual error sequence through {ε (") (k)} ($ to modify the forecast formula of (4), the frequently-used correction methods is the residual sequence modeling method and cycle analysis method (Deng, 1987).

The scope of application of grey prediction model:
From the grey GM (1, 1) model equation, we know that the calculated data from the model has its monotonicity, thus the predictive data that has been reduced back will also have its monotonicity.So the grey GM (1, 1) model has a better effect on simulation and prediction of smooth monotone data, but it is inapplicable to the simulation of non monotone data.

APPLICATION OF GREY FORECASTING MODEL IN THE PREDICTION OF FOOD PRODUCTION IN HUAINAN
Data source: We have continuously collected the annual production data for 20 years in Huainan from 1995 to 2014.The first 16 data is taken as the original data of the model, the remaining 4 data is taken as the object to compare with the prediction results of the grey model and the data is increasing monotonically, as shown in Table 2.
Step 2: The reduced values of the original data of food production in Huainan during 2011-2014 which is obtained by the basic formula of (5) were y (0) (17) = 141.3,y (0) (18) = 134.7,y (0) (19) = 136.3,y (0) (20) = 139.8(Table 3).The test of precision of forecasting numerical value: According to the inspection method of the grey prediction model which has high precision, the predicted values of annual grain output during 2011-2014 in Huainan are tested within the allowable range, so the analysis of residual sequence and the correction of the prediction formula are unnecessary (Fig. 1).

CONCLUSION
According to the monotone increasing characteristics of the annual grain output data in Huainan, the grey GM (1, 1) model is used in this study to forecast grain output from 2011 to 2014.The error is within the allowable range by comparing the results of prediction with the true value and belongs to a small probability event, the prediction has better effect.It also shows that the model to forecast the grain output in Huainan has a certain practical value.

Fig. 1 :
Fig. 1: The comparison chart of annual grain output predicted value with the real value during 2011-2014 in Huainan

Table 1 :
The standard of grade of grey prediction accuracy test

Table 3 :
The predicted results of 2011-2014 annual grain output in Huainan city