Comparative Analysis of Parameter Estimation Methods for Periodic Autoregressive Models with Scale Mixture of Skew Normal Distributions in the Face of Outliers and Heavy Tailed Data

Manouchehri, Tahere; Nematollahi, Ali Reza

doi:10.61186/jss.19.2.10

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Comparative Analysis of Parameter Estimation Methods for Periodic Autoregressive Models with Scale Mixture of Skew Normal Distributions in the Face of Outliers and Heavy Tailed Data

Tahere Manouchehri ^*

, Ali Reza Nematollahi

Abstract: (17 Views)

In this paper, we present a comprehensive review and comparative analysis of estimation methods for periodic autoregressive (PAR) models driven by scale mixture of skew-normal (SMSN) innovations, a flexible class suitable for modeling both symmetric and asymmetric data. Expectation-conditional maximization algorithms are employed to develop maximum likelihood, maximum a posteriori, and Bayesian estimation procedures. A thorough evaluation of these methods is conducted using simulation studies, with particular attention to asymptotic properties and robustness against outliers, high peaks, and heavy tails. To demonstrate their practical utility, these methods are applied to monthly Google stock price data.

Keywords: Periodic autoregressive models, Scale mixture of skew normal, ML estimate, ECM algorithms, MAP estimate, Bayesian analysis, MCMC algorithms, Heavy tails, Outliers.

Full-Text [PDF 8832 kb] (12 Downloads)

Type of Study: Research | Subject: Time Series
Received: 2025/09/24 | Accepted: 2026/09/1

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