Generalized Cauchy difference iterative forecasting model for wind speed based on fractal time series

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.