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In this paper, a wind speed prediction method was proposed based on the maximum Lyapunov exponent (Le) and the fractional Levy stable motion (fLsm) iterative prediction model. First, the calculation of the maximum prediction steps was introduced based on the maximum Le. The maximum prediction steps could provide the prediction steps for subsequent prediction models. Secondly, the fLsm iterative prediction model was established by stochastic differential. Meanwhile, the parameters of the fLsm iterative prediction model were obtained by rescaled range analysis and novel characteristic function methods, thereby obtaining a wind speed prediction model. Finally, in order to reduce the error in the parameter estimation of the prediction model, we adopted the method of weighted wind speed data. The wind speed prediction model in this paper was compared with GA-BP neural network and the results of wind speed prediction proved the effectiveness of the method that is proposed in this paper. In particular, fLsm has long-range dependence (LRD) characteristics and identified LRD by estimating self-similarity index H and characteristic index α. Compared with fractional Brownian motion, fLsm can describe the LRD process more flexibly. However, the two parameters are not independent because the LRD condition relates them by αH > 1.

In this paper, an efficient prediction model based on the fractional generalized Pareto motion (fGPm) with Long-Range Dependent (LRD) and infinite variance characteristics is proposed. Firstly, we discuss the meaning of each parameter of the generalized Pareto distribution (GPD), and the LRD characteristics of the generalized Pareto motion are analyzed by taking into account the heavy-tailed characteristics of its distribution. Then, the mathematical relationship H = 1 / α between the self-similar parameter H and the tail parameter α is obtained. Also, the generalized Pareto increment distribution is obtained using statistical methods, which offers the subsequent derivation of the iterative forecasting model based on the increment form. Secondly, the tail parameter α is introduced to generalize the integral expression of the fractional Brownian motion, and the integral expression of fGPm is obtained. Then, by discretizing the integral expression of fGPm, the statistical characteristics of infinite variance is shown. In addition, in order to study the LRD prediction characteristic of fGPm, LRD and self-similarity analysis are performed on fGPm, and the LRD prediction conditions H > 1 / α is obtained. Compared to the fractional Brownian motion describing LRD by a self-similar parameter H, fGPm introduces the tail parameter α, which increases the flexibility of the LRD description. However, the two parameters are not independent, because of the LRD condition H > 1 / α. An iterative prediction model is obtained from the Langevin-type stochastic differential equation driven by fGPm. The prediction model inherits the LRD condition H > 1 / α of fGPm and the time series, simulated by the Monte Carlo method, shows the superiority of the prediction model to predict data with high jumps. Finally, this paper uses power load data in two different situations (weekdays and weekends), used to verify the validity and general applicability of the forecasting model, which is compared with the fractional Brown prediction model, highlighting the “high jump data prediction advantage” of the fGPm prediction model.

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