Heavy Tail and Long-Range Dependence for Skewed Time Series Prediction Based on a Fractional Weibull Process

In this paper, a fractional Weibull process is utilized in a predictive stochastic differential equation model to allow for skewness and heavy-tailed characteristics. To this aim, a fractional Weibull process with non-Gaussian characteristics and a long memory effect is proposed to drive the predictive stochastic differential equation. The difference iterative forecasting model is proposed as its stochastic difference scheme. The consistency, stability, and convergence of the model are analyzed. In the proposed model, variational mode decomposition is utilized as the data preprocessing approach to separate the stationary and non-stationary components. Actual wind speed data and stock price data are employed in two separate case studies.