Finite Iterative Forecasting Model Based on Fractional Generalized Pareto Motion

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