Mechanism of single variable grey forecasting modelling: Integration of increment and growth rate

Abstract

Grey forecasting models as a kind of time series model have been widely applied in different areas, which have achieved high-precision performance for different series with evolutionary characteristics. This paper aims to deconstruct its modelling mechanism from the perspective of data characteristics. First, classical increment and growth rate relationship is analysed and a unified representation of the mixed relationship with increment and growth rate is given. To establish the relationship between grey forecasting models and traditional models, the mechanism is analysed by deconstructing discrete structural components. Then, the series of evolutionary characteristics in main grey forecasting models are linked and summarized. The affine properties of parameter estimation and predicted value are analysed before simulation. Furthermore, through numerical simulations, the performance of grey forecasting models for different feature sequences and the difference between single variable models is demonstrated. Finally, results in the real case show that MAPEs of grey forecasting models have controlled under 4% for different sequences, which are suitable for mixed feature sequences.