Journal of Statistics Applications & Probability

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This paper utilizes the Gibbs sampling technique to develop a Bayesian inference for Seasonal Moving Average (SMA) model, which includes parameters that distinguish between Multiplicative and Non-multiplicative models (referred to as Augmented Seasonal Moving Average hereafter). The construction of Bayesian inference involves several steps. Firstly, the method of Non-linear least squares (NLS) is used to estimate unknown lagged errors, allowing for the approximation of the complex likelihood function. Secondly, both a semi-conjugate prior distribution and a non- informative prior distribution are applied to the unknown parameters and initial errors. Thirdly, the prior distributions are combined with the approximated likelihood function to obtain the joint posterior distribution. Lastly, the full conditional distributions are derived as part of the Gibbs sampling process. The proposed method is notable for its simplicity in assessing the significance of the parameters that distinguish between Multiplicative and Non-multiplicative models, a task that is challenging to accomplish using classical analysis. The convergence of the method was verified, ensuring that it reached stable and reliable results.

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