Bayesian Identification of Seasonal Multivariate Autoregressive Processes

Abstract

The main objective of this article is to develop an approximate Bayesian procedure to identify the orders of seasonal multivariate autoregressive processes. Using either a matrix normal-Wishart prior density or a non informative prior, which is combined with an approximate conditional likelihood function, the foundation of the proposed technique is to derive the joint posterior mass function of the model orders in a convenient form. Then one may easily evaluate the joint posterior probabilities of all possible values of the model orders and choose the orders at which the joint posterior mass function attains its maximum to be the identified orders. A simulation study, with different prior mass functions, is carried out to determine the effectiveness of the proposed technique in handling the identification problem of the seasonal bivariate autoregressive processes.

إثر التغير في التركيب العمري للعاملين في القطاع الحكومي على الاشتراكات المحصلة لصناديق التأمينات في مصر خلال الفترة من 2020 حتى 2040

“…Theorem: Given n observation 𝑌 = (y , y , … , y )from autoregressive moving average (ARMA) model given by ( 1), an approximate conditional likelihood function in (17) and the joint prior density given by (21), then the approximate marginal posterior probability mass function of the autoregressive moving average orders p and q is Proof: The following procedures can be used to prove the theorem  Multiplying Eq. ( 18) by both Eq.…”

“…Ali (2009) extended the technique proposed by Shaarawy et al (2007) in order to identify the mixed ARMA (p, q) processes. Moreover, the direct approach has been extended to seasonal multivariate AR processes by Shaarawy and Ali [2015]. The direct method for determining the ordering of vector MA models with seasonality has been expanded by Shaarawy et al [2021].…”