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Gray Prediction Model






The grey system theory, established based on “grey box” developed by Julong Deng in 1982, is a new methodology that focuses on the study of problems involving small samples and poor information[3, 4]. The random variables are regarded as grey numbers and the stochastic process is referred to as a grey process for the grey theory. It deals with partially known information through generating, excavating, and extracting useful information from what is available[5, 6]. A grey prediction model is one of the most important parts of grey system theory, and it has been employed in many fields, such as industry[7, 8], agriculture[9], environment[10], and military[11].

The basic idea of the theory of gray system prediction is a known data sequence according to the certain rules to constitute a dynamic and non-dynamic white block, and some kind of transformation or solution to solve future gray model, and then according to some guidelines to gradually improve the whiteness. The main features of the gray prediction model doesn't use its original economic data sequence to predict. The effect of the economic data sequence is shorter and has a clear upward trend[12]. The model is developed in this study.

Model refers to the first order differential equation model of a variable to predict. It is a first-order single sequence of linear dynamic models for time series prediction, and it is also a discrete form of differential equation model. The specific form of it as follows:

(1)

Then the parameters are identified. The equation (1) represents a single variable first-order differential equation of time is continuous. It can be in discrete form as shown below:

(2)

 

Where

(3)

(4)

(5)

Suppose is the calculated result by the formula (2), the parameter can be taken from the following formula:

(6)

Get variables , calculated values is

(7)

GM (1, 1) model is shown above, the formula (7) is the basic conclusions of the GM (1, 1) model.

 

 






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