Abstract
The local irregularity and global correlation of wind speed can be described by the fractal dimension D and the Hurst parameter H. However, the existing mathematical models imply a linear relationship between the fractal dimension D and the Hurst parameter H, which is not adequate to describe the complete characteristics of the wind speed. To overcome the descriptive limitations of the $$D-H$$ linearity assumption, in this paper, we introduce novel model, based on the generalized Cauchy (GC) process, for simulation and forecasting of wind speed. In the model, the fractal dimension D and Hurst parameter H can be combined arbitrarily to describe the local irregularity and global correlation of the wind speed. Furthermore, the GC process is taken as the disturbance fluctuation term in the forecasting model, and a difference iteration form is obtained as difference equation and incremental distribution. In such model, the maximum forecasting range of the wind speed is determined by the maximum Lyapunov exponent. To illustrate the properties of the model and its performance, simulating and forecasting of the actual wind speeds in two regions are reported.
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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