Bayesian Identification of Multivariate Autoregressive Processes

Abstract

Identification is one of the most important stages of a time series analysis. This paper develops a direct Bayesian technique to identify the order of multivariate autoregressive processes. By employing the conditional likelihood function and a matrix normal-Wishart prior density, or Jeffreys' vague prior, the proposed identification technique is based on deriving the exact posterior probability mass function of the model order in a convenient form. Then one may easily evaluate the posterior probabilities of the model order and choose the order that maximizes the posterior mass function to be the suitable order of the time series data being analyzed. Assuming the bivariate autoregressive processes, a numerical study, with different prior mass functions, is carried out to assess the efficiency of the proposed technique. The analysis of the numerical results supports the adequacy of the proposed technique in identifying the orders of multivariate autoregressive processes.

Sensitivity to Prior Specification in Bayesian Identification of Autoregressive Time Series Models

“…Finally, we compute the posterior probabilities and identify the model order with the maximum posterior probability. Results of the KL divergence and its calibration presented in Table ( 14) and results of the posterior probability and identified model are presented in Table ( 15). It can be observed that these results are very consistent with the results from the simulation study in previous subsection, and the identified models are almost the same as those identified by the non-Bayesian approach.…”

“…Following this idea, Diaz and Farah (1981) proposed a Bayesian method to identify the order of autoregressive models. Their work has been extended by many researchers to various time series models, which include moving average models (Shaarawy et al, 2007), autoregressive moving average models (Fan and Yao, 2009), multivariate autoregressive models (Shaarawy and Ali, 2008), and multivariate moving average models (Shaarawy and Ali, 2012). These researchers have employed one or more of the abovementioned prior distributions to derive the posterior mass function of the model order, however, none of them has evaluated the sensitivity of model identification to different types of prior distributions.…”

Bayesian Identification of Seasonal Multivariate Autoregressive Processes

“…On the other hand, the Bayesian techniques to identify multivariate time series have recently been studied. Shaarawy and Ali (2008) Bayesian technique to identify the order of nonseasonal multivariate autoregressive processes. Regarding the seasonal multivariate time series, one may say that a purely Bayesian procedure of identification has not been explored yet.…”

Modeling and Forecasting the Number of Pilgrims Coming from Outside the Kingdom of Saudi Arabia Using Bayesian and Box-Jenkins Approaches

“…Their approach has been extended to the case of moving average processes by Shaarawy et al (2007). The multivariate version of their direct approach has been introduced by Shaarawy and Ali (2008).…”