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Seasonal ARIMA models with a random period

Author

Listed:
  • Aknouche, Abdelhakim
  • Dimitrakopoulos, Stefanos
  • Rabehi, Nadia

Abstract

A general class of seasonal autoregressive integrated moving average models (SARIMA), whose period is an independent and identically distributed random process valued in a finite set, is proposed. This class of models is named random period seasonal ARIMA (SARIMAR). Attention is focused on three subsets of them: the random period seasonal autoregressive (SARR) models, the random period seasonal moving average (SMAR) models and the random period seasonal autoregressive moving average (SARMAR) models. First, the causality, invertibility, and autocovariance shape of these models are revealed. Then, the estimation of the model components (coefficients, innovation variance, probability distribution of the period, (unobserved) sample-path of the random period) is carried out using the Expectation-Maximization algorithm. In addition, a procedure for random elimination of seasonality is developed. A simulation study is conducted to assess the estimation accuracy of the proposed algorithmic scheme. Finally, the usefulness of the proposed methodology is illustrated with two applications about the annual Wolf sunspot numbers and the Canadian lynx data.

Suggested Citation

  • Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos & Rabehi, Nadia, 2025. "Seasonal ARIMA models with a random period," MPRA Paper 127200, University Library of Munich, Germany, revised 06 Dec 2025.
    • Handle: RePEc:pra:mprapa:127200
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    References listed on IDEAS

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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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