Generalized Cauchy Process: Difference Iterative Forecasting Model

• Published in: Fractal and fractional Vol. 5; no. 2; p. 38
• Main Authors: Xing, Jie, Song, Wanqing, Villecco, Francesco
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 2021
• Subjects: Brownian motion; difference iterative forecasting model; Forecasting; fractal dimension; Fractal geometry; Fractals; generalized cauchy process; Hurst parameter; Iterative methods; long-range dependent; Mathematical models; Neural networks; Parameter estimation; Stochastic models; Time series; Wind speed; wind speed forecasting
• ISSN: 2504-3110; 2504-3110
• DOI: 10.3390/fractalfract5020038

The contribution of this article is mainly to develop a new stochastic sequence forecasting model, which is also called the difference iterative forecasting model based on the Generalized Cauchy (GC) process. The GC process is a Long-Range Dependent (LRD) process described by two independent parameters: Hurst parameter H and fractal dimension D. Compared with the fractional Brownian motion (fBm) with a linear relationship between H and D, the GC process can more flexibly describe various LRD processes. Before building the forecasting model, this article demonstrates the GC process using H and D to describe the LRD and fractal properties of stochastic sequences, respectively. The GC process is taken as the diffusion term to establish a differential iterative forecasting model, where the incremental distribution of the GC process is obtained by statistics. The parameters of the forecasting model are estimated by the box dimension, the rescaled range, and the maximum likelihood methods. Finally, a real wind speed data set is used to verify the performance of the GC difference iterative forecasting model.