Seasonal ARIMA models with a random period

Abdelhakim Aknouche, Stefanos Dimitrakopoulos and Nadia Rabehi

MPRA Paper from University Library of Munich, Germany

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.

Keywords: EM algorithm; irregular seasonality; non-integer period; random period; random period seasonal ARMA models. (search for similar items in EconPapers)
JEL-codes: C10 C18 C22 (search for similar items in EconPapers)
Date: 2025-12-06, Revised 2025-12-06
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