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.