IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-02901595.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: https://hal.umontpellier.fr/hal-02901595/document
    Download Restriction: no
    File URL: https://libkey.io/10.1142/S1793005721500101?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    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. 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.
    4. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Alfred Mbairadjim Moussa & Jules Sadefo Kamdem, 2022. "A fuzzy multifactor asset pricing model," Annals of Operations Research, Springer, vol. 313(2), pages 1221-1241, June.
    3. Dobrislav Dobrev∗ & Travis D. Nesmith & Dong Hwan Oh, 2017. "Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors," JRFM, MDPI, vol. 10(1), pages 1-14, February.
    4. Evangelos Vasileiou, 2022. "Inaccurate Value at Risk Estimations: Bad Modeling or Inappropriate Data?," Computational Economics, Springer;Society for Computational Economics, vol. 59(3), pages 1155-1171, March.
    5. Jaworski, Piotr & Liberadzki, Kamil & Liberadzki, Marcin, 2017. "How does issuing contingent convertible bonds improve bank's solvency? A Value-at-Risk and Expected Shortfall approach," Economic Modelling, Elsevier, vol. 60(C), pages 162-168.
    6. 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.
    7. Qasim Noor & Tabasam Rashid & Syed Muhammad Husnine, 2021. "An extended TDM method under probabilistic interval-valued hesitant fuzzy environment for stock selection," PLOS ONE, Public Library of Science, vol. 16(5), pages 1-24, May.
    8. Pedro Antonio Martín-Cervantes & María del Carmen Valls Martínez, 2023. "Unraveling the relationship between betas and ESG scores through the Random Forests methodology," Risk Management, Palgrave Macmillan, vol. 25(3), pages 1-29, September.
    9. Christian Biener & Martin Eling, 2013. "Recent Research Developments Affecting Nonlife Insurance—The CAS Risk Premium Project 2012 Update," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 16(2), pages 219-231, September.
    10. Qingsong Mao & Huan Huang, 2021. "Interval Ranges of Fuzzy Sets Induced by Arithmetic Operations Using Gradual Numbers," Mathematics, MDPI, vol. 9(12), pages 1-15, June.
    11. Sun, Yuying & Zhang, Xinyu & Wan, Alan T.K. & Wang, Shouyang, 2022. "Model averaging for interval-valued data," European Journal of Operational Research, Elsevier, vol. 301(2), pages 772-784.
    12. R. Sujatha & T. M. Rajalaxmi, 2016. "Hierarchical Fuzzy Hidden Markov Chain for Web Applications," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 83-118, January.
    13. Debdas Ghosh, 2016. "A Newton method for capturing efficient solutions of interval optimization problems," OPSEARCH, Springer;Operational Research Society of India, vol. 53(3), pages 648-665, September.
    14. Sankar Prasad Mondal & Tapan Kumar Roy, 2017. "Solution of second order linear fuzzy ordinary differential equation by Lagrange multiplier method with application in mechanics," OPSEARCH, Springer;Operational Research Society of India, vol. 54(4), pages 766-798, December.
    15. Luciano Stefanini & Barnab?s Bede, 2012. "Some notes on generalized Hukuhara differentiability of interval-valued functions and interval differential equations," Working Papers 1208, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2012.
    16. Luciano Stefanini & Barnab?s Bede, 2012. "Generalized Fuzzy Differentiability with LU-parametric Representation," Working Papers 1210, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2012.
    17. Pablo J. Villacorta & Laura González-Vila Puchades & Jorge de Andrés-Sánchez, 2021. "Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance," Mathematics, MDPI, vol. 9(4), pages 1-23, February.
    18. 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.
    19. Chikashi Tsuji, 2017. "A Non-linear Estimation of the Capital Asset Pricing Model: The Case of Japanese Automobile Industry Firms," Applied Finance and Accounting, Redfame publishing, vol. 3(2), pages 20-26, August.
    20. 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.

    More about this item

    Keywords

    Wold décomposition; stationary time series; interval-valued time series processes; ARMA model;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-02901595. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.