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Fractional Lévy stable motion: Finite difference iterative forecasting model

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  • Liu, He
  • Song, Wanqing
  • Li, Ming
  • Kudreyko, Aleksey
  • Zio, Enrico

Abstract

In this study we use the fractional Lévy 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 Lévy 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.

Suggested Citation

  • Liu, He & Song, Wanqing & Li, Ming & Kudreyko, Aleksey & Zio, Enrico, 2020. "Fractional Lévy stable motion: Finite difference iterative forecasting model," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    • Handle: RePEc:eee:chsofr:v:133:y:2020:i:c:s096007792030031x
    DOI: 10.1016/j.chaos.2020.109632
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    References listed on IDEAS

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    1. Song, Wanqing & Li, Ming & Li, Yuanyuan & Cattani, Carlo & Chi, Chi-Hung, 2019. "Fractional Brownian motion: Difference iterative forecasting models," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 347-355.
    2. Jumarie, Guy, 2005. "Merton's model of optimal portfolio in a Black-Scholes Market driven by a fractional Brownian motion with short-range dependence," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 585-598, December.
    3. Aleksander Janicki & Aleksander Weron, 1994. "Can One See Alpha-stable Variables and Processes?," HSC Research Reports HSC/94/01, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    4. Longjin, Lv & Ren, Fu-Yao & Qiu, Wei-Yuan, 2010. "The application of fractional derivatives in stochastic models driven by fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4809-4818.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    6. Li, Ming, 2017. "Record length requirement of long-range dependent teletraffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 472(C), pages 164-187.
    7. Zanzotto, P. A., 1997. "On solutions of one-dimensional stochastic differential equations driven by stable Lévy motion," Stochastic Processes and their Applications, Elsevier, vol. 68(2), pages 209-228, June.
    8. Song, Wanqing & Cattani, Carlo & Chi, Chi-Hung, 2020. "Multifractional Brownian motion and quantum-behaved particle swarm optimization for short term power load forecasting: An integrated approach," Energy, Elsevier, vol. 194(C).
    9. Soumendra N. Lahiri & Ujjwal Das & Daniel J. Nordman, 2019. "Empirical Likelihood for a Long Range Dependent Process Subordinated to a Gaussian Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(4), pages 447-466, July.
    10. Song Wanqing & Xiaoxian Chen & Carlo Cattani & Enrico Zio, 2020. "Multifractional Brownian Motion and Quantum-Behaved Partial Swarm Optimization for Bearing Degradation Forecasting," Complexity, Hindawi, vol. 2020, pages 1-9, January.
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