Abstract
The nonhomogeneous grey model has been seen as an effective method for forecasting time series with approximate nonhomogeneous index law, which has been widely used in diverse disciplines on account of its high prediction precision. However, there remains room for improvements. For this, this study presents an improved nonhomogeneous grey model by incorporating the dynamic integral mean value theorem and fractional accumulation simultaneously. In order to promote the efficacy of the optimised model, we apply the whale optimization algorithm (WOA) to ascertain its optimal parameter. In particular, two examples are conducted to validate the superiority of the proposed model in contrast with other benchmarks, and the experimental results show that the mean absolute percentage error of the proposed approach is 808692% and 6.0706%, respectively, indicating the proposed approach performs better than other competing models.
Highlights
Journal of MathematicsConsidering the vital impact of the background value on the prediction performance of the nonhomogeneous grey model, Zeng and Liu [18] presented an improved nonhomogeneous grey model based on fractional-order accumulation, which can achieve high accurate prediction by virtue of fractional-order accumulation
There exist a variety of nonhomogeneous grey models; these approaches are not universal. at is, many optimization approaches are only suitable for special cases. e optimization methods for increasing the prediction precision of the grey models include fractional accumulation and integral median theorem aiming to optimize the background value
We observe from the modeling procedure above that the prediction precision is dependent on the system parameters influenced by the background value and cumulative sum operator
Summary
Considering the vital impact of the background value on the prediction performance of the nonhomogeneous grey model, Zeng and Liu [18] presented an improved nonhomogeneous grey model based on fractional-order accumulation, which can achieve high accurate prediction by virtue of fractional-order accumulation. Wu et al [19] established a discrete nonhomogeneous grey model based on fractional-order accumulation. E optimization methods for increasing the prediction precision of the grey models include fractional accumulation and integral median theorem aiming to optimize the background value. On the foundation of the previous knowledge, this study constructs a novel discrete nonhomogeneous grey model by incorporating the idea of fractional accumulation and the dynamic integral median theorem; the composite grey model (denoted as FDNGM(1,1) for short) is developed thereby, which can fit diverse series sequence through altering the fractional accumulation order and backgroundvalue coefficients. We apply the fractional accumulation and dynamic integral median theorem on the modeling procedure for improving the prediction capacity of the existing nonhomogeneous model
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