Inspecting a seasonal ARIMA model with a random period

Aknouche, Abdelhakim and Rabehi, Nadia (2024): Inspecting a seasonal ARIMA model with a random period.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Seasonal ARIMA models, irregular seasonality, random period, non-integer period, SARIMAR model, EM algorithm.
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C18 - Methodological Issues: General; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection

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