Abstract
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.
Highlights
IntroductionPublisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations
A large number of experiments prove that the forecasting methods based on regression analysis [5,6], Gray system [7,8,9], Wiener process [10,11], Markov process [12,13,14], support vector machine [15,16], fuzzy analysis [17,18], and neural network [19,20] cannot describe the Long-Range Dependent (LRD) characteristics in the forecasting process of the actual stochastic sequences, which leads in low accuracy of forecasting results
Conclusions parameter model generalized Cauchy process and it is applied to the changing trend of
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. It is worth noting that the existing stochastic models describe LRD characteristics with a single parameter, e.g., the Hurst parameter H in the fBm [36], or the fractal dimension D [23,37]. The fBm and the fractional Levy stable motions are greatly limited in describing the local irregularities and LRD characteristics of stochastic sequences. In the GC process, the Hurst parameter H is used to describe the global properties of stochastic sequences, e.g., LRD characteristics; the fractal dimension D describes local properties, e.g., local irregularities. A financial stock price prediction model established by fBm as the interference term of the Ito process is proposed, namely the fractional Black-Scholes model [43,44,45], to predict the trend of stock prices, the methods and ideas of the fBmdriven Ito process applied to financial forecasting are combined.
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