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S-ARMA model and Wold decomposition for covariance stationary interval-valued time series processes

Author

Listed:
  • Jules Sadefo-Kamdem

    (MRE - Montpellier Recherche en Economie - UM - Université de Montpellier)

  • Babel Raïssa Guemdjo Kamdem

    (IMSP - Institut de Mathématiques et de Sciences Physiques - UAC - Université d’Abomey-Calavi = University of Abomey Calavi)

  • Carlos Ougouyandjou

    (MRE - Montpellier Recherche en Economie - UM - Université de Montpellier)

Abstract

The main purpose of this work is to contribute to the study of set-valued random variables by providing a kind of Wold decomposition theorem for interval-valued processes. As the set of set-valued random variables is not a vector space, the Wold decomposition theorem as established in 1938 by Herman Wold is not applicable for them. So, a notion of pseudovector space is introduced and used to establish a generalization of the Wold decomposition theorem that works for interval-valued covariance stationary time series processes. Before this, set-valued autoregressive moving-average (S-ARMA) time series process is defined by taking into account an arithmetical difference between random sets and random real variables.

Suggested Citation

  • Jules Sadefo-Kamdem & Babel Raïssa Guemdjo Kamdem & Carlos Ougouyandjou, 2021. "S-ARMA model and Wold decomposition for covariance stationary interval-valued time series processes," Post-Print hal-02901595, HAL.
    • Handle: RePEc:hal:journl:hal-02901595
    DOI: 10.1142/S1793005721500101
    Note: View the original document on HAL open archive server: https://hal.umontpellier.fr/hal-02901595
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    References listed on IDEAS

    as
    1. Mbairadjim Moussa, A. & Sadefo Kamdem, J. & Terraza, M., 2014. "Fuzzy value-at-risk and expected shortfall for portfolios with heavy-tailed returns," Economic Modelling, Elsevier, vol. 39(C), pages 247-256.
    2. Wang, Xun & Zhang, Zhongzhan & Li, Shoumei, 2016. "Set-valued and interval-valued stationary time series," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 208-223.
    3. Mbairadjim Moussa, A. & Sadefo Kamdem, J. & Shapiro, A.F. & Terraza, M., 2014. "CAPM with fuzzy returns and hypothesis testing," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 40-57.
    4. Sadefo Kamdem, J. & Mbairadjim Moussa, A. & Terraza, M., 2012. "Fuzzy risk adjusted performance measures: Application to hedge funds," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 702-712.
    5. Luciano Stefanini, 2008. "A generalization of Hukuhara difference for interval and fuzzy arithmetic," Working Papers 0801, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2008.
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    Cited by:

    1. Babel Raïssa Guemdjo Kamdem & Jules Sadefo-Kamdem & Carlos Ougouyandjou, 2020. "On Random Extended Intervals and their ARMA Processes," Working Papers hal-03169516, HAL.
    2. Babel Raïssa Guemdjo Kamdem & Jules Sadefo-Kamdem & Carlos Ogouyandjou, 2021. "An Abelian Group way to study Random Extended Intervals and their ARMA Processes," Working Papers hal-03174631, HAL.

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    Keywords

    Wold décomposition; stationary time series; interval-valued time series processes; ARMA model;
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