Journal
CHAOS SOLITONS & FRACTALS
Volume 133, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2020.109632
Keywords
Fractional Levy stable motion; Long-range dependence; Stochastic differential equation; Forecasting model
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Funding
- National Natural Science Foundation of China NSFC [61672238, 61272402]
- Natural Science Foundation of Shanghai [14ZR1418500]
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In this study we use the fractional Levy stable motion (fLsm) to establish a finite iterative forecasting model with Long Range Dependent (LRD) characteristics. The LRD forecasting model considers the influence of current and past trends in stochastic sequences on future trends. We find that the discussed model can accurately forecast the trends of stochastic sequences. This fact enables us to introduce the fLsm as the fractional-order model of Levy stable motion. Self-similarity and LRD characteristics of the flsm model is introduced by using the relationship between self-similar index and the characteristic index. Thus, the order Stochastic Differential Equation (FSDE) which describes the fLsm can be obtained. The parameters of the FSDE were estimated by using a novel characteristic function method. The forecasting model with the LRD characteristics was obtained by discretization of FSDE. The Monte Carlo method was applied to demonstrate the feasibility of the forecasting model. The power load forecasting history data demonstrates the advantages of our model. (C) 2020 Elsevier Ltd. All rights reserved.
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