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Inspecting a seasonal ARIMA model with a random period

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Listed:
  • Aknouche, Abdelhakim
  • Rabehi, Nadia

Abstract

This work proposes a class of seasonal autoregressive integrated moving average models whose period is an independent and identically distributed random process valued in a finite set. The causality, invertibility, and autocovariance shape of the model are first revealed. Then, the estimation of the parameters which are the model coefficients, the innovation variance, the probability distribution of the period, and the (unobserved) sample-path of the period, is carried out using the expectation-maximization algorithm. In particular, a procedure for random elimination of seasonality is proposed. An application of the methodology to the annual Wolfer sunspot numbers is provided.

Suggested Citation

  • Aknouche, Abdelhakim & Rabehi, Nadia, 2024. "Inspecting a seasonal ARIMA model with a random period," MPRA Paper 120758, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:120758
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    References listed on IDEAS

    as
    1. Yonas Gebeyehu Tesfaye & Paul L. Anderson & Mark M. Meerschaert, 2011. "Asymptotic results for Fourier‐PARMA time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(2), pages 157-174, March.
    2. Eduardo Rossi & Dean Fantazzini, 2015. "Long Memory and Periodicity in Intraday Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 13(4), pages 922-961.
    3. Ambach, Daniel & Schmid, Wolfgang, 2015. "Periodic and long range dependent models for high frequency wind speed data," Energy, Elsevier, vol. 82(C), pages 277-293.
    4. Ilias Tsiakas, 2006. "Periodic Stochastic Volatility and Fat Tails," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 90-135.
    5. Aknouche, Abdelhakim & Guerbyenne, Hafida, 2009. "On some probabilistic properties of double periodic AR models," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 407-413, February.
    6. Ziel, Florian & Croonenbroeck, Carsten & Ambach, Daniel, 2016. "Forecasting wind power – Modeling periodic and non-linear effects under conditional heteroscedasticity," Applied Energy, Elsevier, vol. 177(C), pages 285-297.
    7. Franses, Philip Hans & Paap, Richard, 2004. "Periodic Time Series Models," OUP Catalogue, Oxford University Press, number 9780199242030.
    8. Hylleberg, S. (ed.), 1992. "Modelling Seasonality," OUP Catalogue, Oxford University Press, number 9780198773184.
    9. Abdelhakim Aknouche & Bader Almohaimeed & Stefanos Dimitrakopoulos, 2022. "Periodic autoregressive conditional duration," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(1), pages 5-29, January.
    10. Philip Hans Franses & Richard Paap, 2011. "Random‐coefficient periodic autoregressions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 65(1), pages 101-115, February.
    11. Ziel, Florian & Steinert, Rick & Husmann, Sven, 2015. "Efficient modeling and forecasting of electricity spot prices," Energy Economics, Elsevier, vol. 47(C), pages 98-111.
    12. Abdelhakim Aknouche & Christian Francq, 2022. "Stationarity and ergodicity of Markov switching positive conditional mean models," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 436-459, May.
    13. Abdelhakim Aknouche & Nadia Rabehi, 2010. "On an independent and identically distributed mixture bilinear time‐series model," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 113-131, March.
    14. Franses, Philip Hans, 1996. "Periodicity and Stochastic Trends in Economic Time Series," OUP Catalogue, Oxford University Press, number 9780198774549.
    15. Ghysels,Eric & Osborn,Denise R., 2001. "The Econometric Analysis of Seasonal Time Series," Cambridge Books, Cambridge University Press, number 9780521565882.
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    More about this item

    Keywords

    Seasonal ARIMA models; irregular seasonality; random period; non-integer period; SARIMAR model; EM algorithm.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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