Bayesian identification of double seasonal autoregressive time series models

Abstract

ABSTRACTSeasonal autoregressive (SAR) models have been modified and extended to model high frequency time series characterized by exhibiting double seasonal patterns. Some researchers have introduced Bayesian inference for double seasonal autoregressive (DSAR) models; however, none has tackled the problem of Bayesian identification of DSAR models. Therefore, in order to fill this gap, we present a Bayesian methodology to identify the order of DSAR models. Assuming the model errors are normally distributed and using three priors, i.e. natural conjugate, g, and Jeffreys’ priors, on the model parameters, we derive the joint posterior mass function of the model order in a closed-form. Accordingly, the posterior mass function can be investigated and the best order of DSAR model is chosen as a value with the highest posterior probability for the time series being analyzed. We evaluate the proposed Bayesian methodology using simulation study, and we then apply it to real-world hourly internet amount of traffic dataset.