The Study Of Forecast Of The Change Of Arable Land Based On Optimization Of GM (1, 1)

Land is one of the most important natural resources. Thus, it is certain that arable land as the essence of land is being focused on, which has deeply influenced development of agriculture and become one of the key factors for a regional development, and in a sense ,even determined whether national economy is sustainable. Furthermore, how to forecast it precisely is playing an important role in land use planning of a government, which can provide some references for harmonizing land use between different industries.The reliability of a forecast result depends on to a great degree whether a forecast method is reasonable. But an objective physical prototype about the change of arable land cannot be found, its mechanism cannot be deeply understood and the difference between factors is difficultly distinguished, we are often reluctant to resort to a statistic method. In contrast, the grey system theory has originality in model establishing, data processing and forecasting, and so on. In fact, according to a separate time series data, by approximately establishing a continuous differential equation, we can reveal the change tendency of system. Moreover, because it is not a statistical method, it is more practical under the condition of few acquired data.Therefore, according to the grey system theory, we established GM(1,1)to forecast the change of arable land of Wuhu City based on its statistical data (1,949-2,003).However, considering the process of returning to original value from forecast value, which will increase error, we further optimized GM(1, 1) in order to obtain its revised model. It is as follows:1. The residual error model of GM (1,1) is more practical than GM(1, 1).There are two reasons: (1)GM (1,1) may be unqualified when it is examined;(2)the residual error model as a supplement for GM(1, 1)can forecast more precisely. 2. Partition modeling, not only conforms to physical laws, but also meets the requirement of GM (1, 1) for a primitive sequence data. Generally speaking, after accumulating to the primary data, we can obtain a stronger regular curve, with a exponential rule. However, a waved rule also appears as a result of all kinds of factors weakening the gradual rule of system. Therefore, to improve the precision of forecast, we carried on partition modeling by combining with the established linear regression model.3. Grey-Markov modeling, with a view to the respective advantages of GM(1,1) and Markov chain model, can carry on forecasting more precisely. On the whole, the advantage of GM(1,1) lies in the short-term forecast ,but its shortcoming is that it does not well deal with the long-term forecast, especially a fluctuating process. By contrast with GM(1,1),the advantage of Markov chain model embodies the long-term forecast with a stochastic but stable process. In fact, although the stochastic but stable process hardly exists, we can perform Grey-Markov modeling by combining GM(1,l) with Markov chain model, because the present state of system Markov chain model deals with is not influenced by the past state of system. Therefore, by the Grey-Markov modeling, the forecast results are more reasonable and practical.4. The optimized model makes the example confirmation in the forecast, the precision conforms to the reality.In a word, we believe that by optimizing GM (1,1) step by step, forecast of the change tendency of arable land of Wuhu City should be more reliable.