The Study on Agricultural Economy Forecasting using Grey Relationship Model

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Abstract. Thinking of grey group model is the improvement on the traditional grey model. It does not merely use a grey model as the ultimate basis， but takes full account of the traditional GM （1，1） model and the GM （1， n） model and join two predictions to form a prediction interval. So， the results are more reasonable and more realistic requirements and have strong guidance and reference. The farther the forecast period is， the worse the forecast is. The forecasts in the forecast period of 1-3 Years are the best， but the results of long-term are only as a reference value and the guidance data. Therefore， as the forecast period goes on， rolling grey model is used to increase accuracy.

Keywords： agricultural economy； grey relation grade； grey model

I. INTRODUCTION

From the current domestic and international documents， few studies have agricultural economic forecast and only a few articles related aspects and agricultural relationship between agricultural rationalizations， but the drawback is that no team verification and compared the forecast.

Therefore， in the existing literature on the basis of analysis， this paper puts forward the application of grey forecasting model group development， analyzes the agricultural economic case， and the result is satisfactory.

There are three reasons. First of all， the agricultural economy is by many uncertain factors. So， agricultural systems can be viewed as a grey system. Second， reduce the requirement of data more suitable for farming. Third， if GM （1， 1） use， considerations and prediction is relatively simple and big mistake appear in the forecast period.

II. GREY RELATIONSHIP MODEL

A. Non-dimensional Data Processing

Because everybody has different data unit's reference sequence of comparison between and sequence， the original series need non-dimensional treatment. Commonly used methods are： initial value method， the mean value method and the interval method （see formula 1， 2， and 3）. After non-dimension treatment， the new matrix can be processed， and then the next step to calculate.

（1）

（2）

（3）

B. Calculating Correlation Coefficient

The first step： calculating the absolute value between each comparative sequence and each reference sequence， that is

The second step： identifying

The third step： calculating correlation coefficient

（4）

Where ？籽 is the resolution ratio which of value is between 0 and 1， the smaller ？籽 is， the larger difference is， and vice versa. Usually ？籽 =0.5.

C. Evaluating

The first step： calculating grey correlation

（5）

The second step： calculating

In terms of above calculation， correlation can be taken. If correlation is the more， the relationship between the two is closer and the degree of influence on Xi is bigger， and vice versa.

III. GREY MODEL

A. GM（1，1）

Grey model， that is， differential equation is established after historical data series is generated. For the system is polluted by noise， historical data is in chaos. These data， that is， grey series or grey process， are modeled through the process of grey， which is known as the grey model. [1]

Defining x （0） as original data series

Generating first-order accumulated series through 1-AGO process

Where

Establishing matrix equation

（6）

Simplifying

（7）

Resolving

（8）

Grey forecasting model is calculating as

（9）

B. GM（1，n）

GM （1， n） represents the establishment of grey model about n variables with first-order differential equations.

Thinking the variables， ， that is，

Accumulated series， that is，

Constructing the first-order linear differential equations

（10）

can be derived according to OLS method， the formula is

（11）

Where

Solution

（12）

（13）

IV. TEST OF GREY MODEL

A. Residual Test

Absolute error sequence

（14）

Relative error sequence

（15）

B. Posterior Difference Test

Posterior deviation is to make a reasonable assessment on the standard level of accuracy in accordance with two indicators-C and P （small error probability）. The standard level is shown in Table 1. In table 1， C is the variance ratio， that is， C=S2/S1， where S1 is the variance of the original data and S2 is the variance of residuals.

Where

TABLE I. GRADES OF TEST INDICATORS

V. CASE study

A. Grey Relation Analysis

In this paper， an area in China as an example can be analyzed. Selected series are primary industry added values（X0）， agricultural added values （X1）， livestock added values （X2）， the added values of aquatic products （X3） forest added values （X4） （ Table II shown）.

TABLE II. AGRICULTURAL STRUCTURE

UNIT： BILLION YUAN

Source： 2003-2008 Statistical Yearbook of this region

Because of the same dimensions of different sequences， the data are not conducted.

The fires step： using formula4 to calculate the grey relation coefficient；

The second step： Using formula5 to calculate and estimate the grey correlation （Table III shown）.

TABLE III. COMPARISON OF GREY RELATIONS

From table 3 the values of ？酌01 ， ？酌02 are more than the values of ？酌03， ？酌04， which shows that the developments of agriculture and livestock industry have a strong correlation with the development of primary industry. So， agricultural added values （X1）， livestock added values （X2） can be selected as the main variables.

B. Establishing GM（1，1）

Formula8，9 can be used to establish GM（1，1）. Conclusion

TABLE IV. FORECAST OF GM（1，1）

Testing

So， the accuracy is “Good”. The model can be used to forecast the agricultural economy from 2010 to 2020（Table ？ shown）.

C. Establishing GM（1，3）

Using formula10，11，12，13 to establish GM（1，3）.

Conclusion

TABLE V. FORECASTS OF GM（1，3）

Unit： billion yuan

Testing

VI. CONCLUSION

Future research is as follows. Firstly， industrial policies in different periods are brought into the research. Secondly， it extends the study to more areas so as to verify the accuracy and rationality of grey group model. Thirdly， the improved model is used to be more in-depth study on the agricultural economic development.

References

[1] Hu Guang-yu. Strategy： Forecast and Decision. Beijing： Tsinghua University Press， 2005， pp.83-117 （In Chinese）

[2] Jiang Hui-ming， Gu Li-li. Strategy of maize's concentr ating to advantage areas in Jilin Province. Chinese Geog raphical Science. 2003（12）.

[3] Yu Zhanping. Agriculture Comparative Advantage Theo ry in New Stage and Empirical Research about Tianjin. China Rural Economy. 2003（9）.

[4] Justin Yifu Lin & Fang Cai & Zhou Li， 1994. "China's economic reforms ： pointers for other economies in transition？，" Policy Research Working Paper Series 1310， The World Bank.

[5] Justin Lifu Lin， 2004. "Development strategy， Transition and Challenges of Development in Lagging regions，" Development Economics Working Papers 447， East Asian Bureau of Economic Research..

[6] Justin Lifu Lin， 2004. "Development Strategies for Inclusive Growth in Developing Asia，" Development Economics Working Papers 444， East Asian Bureau of Economic Research.

[7] Lin， Justin Yifu， 2003. "Development Strategy， Viability， and Economic Convergence，" Economic Development and Cultural Change， University of Chicago Press， vol. 51（2）， pages 276-308.