BAYESIAN-ANALYSIS OF VECTOR ARMA MODELS USING GIBBS SAMPLING

We present a methodology for estimation, prediction, and model assessm ent of vector autoregressive moving-average (VARMA) models in the Baye sian framework using Markov chain Monte Carlo algorithms. The sampling -based Bayesian framework for inference allows for the incorporation o f parameter restrictions, such as stationarity restrictions or zero co nstraints, through appropriate prior specifications. It also facilitat es extensive posterior and predictive analyses through the use of nume rical summary statistics and graphical displays, such as box plots and density plots for estimated parameters. We present a method for compu tationally feasible evaluation of the joint posterior density of the m odel parameters using the exact likelihood function, and discuss the u se of backcasting to approximate the exact likelihood function in cert ain cases. We also show how to incorporate indicator variables as addi tional parameters for use in coefficient selection. The sampling is fa cilitated through a Metropolis-Hastings algorithm. Graphical technique s based on predictive distributions are used for informal model assess ment. The methods are illustrated using two data sets from business an d economics. The first example consists of quarterly fixed investment, disposable income, and consumption rates for West Germany, which are known to have correlation and feedback relationships between series. T he second example consists of monthly revenue data from seven differen t geographic areas of IBM. The revenue data exhibit seasonality, stron g inter-regional dependence, and feedback relationships between certai n regions. (C) 1997 by John Wiley & Sons, Ltd.