Study On The Coupling Model Of Grey System GM (1,1) And Trigonometric Function

Subjects: Mathematics >> Modeling and Simulation submitted time 2021-04-23

倪嘉雨 叶林峰 高德宏 邓洋

Abstract： Grey system model is widely used in mathematical modeling and approximate calculation because of its simplicity and clear mathematical background. The principle of grey system model can be summarized as the use of time response function to simulate the evolution of data series. Among them, GM (1,1) model is the most basic and can reflect the idea of grey modeling most widely. The time response function of the traditional GM (1,1) model is constructed by the exponent of natural constant . Also, for this characteristic, the GM (1,1) model has strong limitations. In practical application, people often modify the time response function of GM (1,1) model. One of the most important correction methods is to couple the original time response function with other functions that can describe the properties of data series. For example, for data series with certain periodicity or quasi periodicity, the original time response function can be coupled with trigonometric function to form GM (1,1) - trigonometric function coupling model. In this paper, the feasibility of this model is deeply discussed, and the estimation method of the parameters in the time response function of the coupled model and the error analysis are proposed.

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