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A Three-Stage Nonparametric Kernel-Based Time Series Model Based on Fuzzy Data

Author

Listed:
  • Gholamreza Hesamian

    (Department of Statistics, Payame Noor University, Tehran 19395-3697, Iran)

  • Arne Johannssen

    (Faculty of Business Administration, University of Hamburg, 20146 Hamburg, Germany)

  • Nataliya Chukhrova

    (HafenCity University of Hamburg, 20457 Hamburg, Germany)

Abstract

In this paper, a nonlinear time series model is developed for the case when the underlying time series data are reported by L R fuzzy numbers. To this end, we present a three-stage nonparametric kernel-based estimation procedure for the center as well as the left and right spreads of the unknown nonlinear fuzzy smooth function. In each stage, the nonparametric Nadaraya–Watson estimator is used to evaluate the center and the spreads of the fuzzy smooth function. A hybrid algorithm is proposed to estimate the unknown optimal bandwidths and autoregressive order simultaneously. Various goodness-of-fit measures are utilized for performance assessment of the fuzzy nonlinear kernel-based time series model and for comparative analysis. The practical applicability and superiority of the novel approach in comparison with further fuzzy time series models are demonstrated via a simulation study and some real-life applications.

Suggested Citation

  • Gholamreza Hesamian & Arne Johannssen & Nataliya Chukhrova, 2023. "A Three-Stage Nonparametric Kernel-Based Time Series Model Based on Fuzzy Data," Mathematics, MDPI, vol. 11(13), pages 1-17, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2800-:d:1176516
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    References listed on IDEAS

    as
    1. Nataliya Chukhrova & Arne Johannssen, 2021. "Stochastic Claims Reserving Methods with State Space Representations: A Review," Risks, MDPI, vol. 9(11), pages 1-55, November.
    2. Coppi, Renato & D'Urso, Pierpaolo & Giordani, Paolo & Santoro, Adriana, 2006. "Least squares estimation of a linear regression model with LR fuzzy response," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 267-286, November.
    3. Abhishekh & Surendra Singh Gautam & S. R. Singh, 2018. "A Score Function-Based Method of Forecasting Using Intuitionistic Fuzzy Time Series," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 91-111, March.
    4. Nataliya Chukhrova & Arne Johannssen, 2017. "State Space Models and the K alman -Filter in Stochastic Claims Reserving: Forecasting, Filtering and Smoothing," Risks, MDPI, vol. 5(2), pages 1-23, May.
    5. Yu, Hui-Kuang, 2005. "Weighted fuzzy time series models for TAIEX forecasting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(3), pages 609-624.
    6. Torbat, Sheida & Khashei, Mehdi & Bijari, Mehdi, 2018. "A hybrid probabilistic fuzzy ARIMA model for consumption forecasting in commodity markets," Economic Analysis and Policy, Elsevier, vol. 58(C), pages 22-31.
    7. Xiangfeng Yang & Baoding Liu, 2019. "Uncertain time series analysis with imprecise observations," Fuzzy Optimization and Decision Making, Springer, vol. 18(3), pages 263-278, September.
    8. Hongjun Guan & Zongli Dai & Aiwu Zhao & Jie He, 2018. "A novel stock forecasting model based on High-order-fuzzy-fluctuation Trends and Back Propagation Neural Network," PLOS ONE, Public Library of Science, vol. 13(2), pages 1-15, February.
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    Cited by:

    1. Gholamreza Hesamian & Faezeh Torkian & Arne Johannssen & Nataliya Chukhrova, 2023. "An Exponential Autoregressive Time Series Model for Complex Data," Mathematics, MDPI, vol. 11(19), pages 1-12, September.

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