ABSTRACT

The study proposed a Stochastic Search Variable Selection Diffuse (SSVS-Diffuse) method for selecting restriction in Vector Autoregressive (VAR) models. This was done by eliciting a new class of Stochastic Search Variable Selection (SSVS) prior using diffuse prior for the variance covariance which allows for non-diagonal treatment of the variance covariance matrix.  The performance of the SSVS-Diffuse was evaluated using a Monte Carlo experiment with 50 replications after deriving the posterior distribution which have no closed form solution. The study generated different sample sizes of VAR, namely T=50,100, 200 and 500 from a two variable, three variable and four variable VAR models with VAR order set at one, VAR(1), two, VAR(2), three, VAR(3) and four, VAR(4) and these models were fitted. The VAR model was simulated from a Multivariate Normal distribution under two scenarios when the variables were independent and when the variables were correlated with various levels of correlations; very high, , high, , moderate, and low . The forecast performance of these scenarios were evaluated in two ways depending on the type of forecast. For the point forecast, the Mean Square Forecast Error (MSFE) was used as the performance measure and for the density forecast the energy score, a multivariate performance measure was used since VAR models are multivariate models. The SSVS-Diffuse prior outperformed the existing Bayesian VAR and classical VAR models namely classical VAR, Minnesota, SSVS-SSVS and SSVS-Wishart in terms of density forecast with minimum energy scores. The study further applied SSVS-Diffuse using the posterior inclusion probability to determine the VAR coefficients that are important to be included in the model. The optimal lags obtained using the SSVS-Diffuse were compared to the optimal lags obtained using classical methods of selecting lag order such as, Final prediction error (FPE), Akaike Information Criterion (AIC), Schwarz information criterion (SC), Sequential modified LR test statistic (each test at 5% level) (LR) and Hannan-Quinn information criterion (HQ).In all the cases considered, the posterior inclusion probability of SSVS-Modified correctly identified the optimal lags. The classical method exhibits fluctuations with SC and HC failing in some cases considered. The Study concludes by applying SSVS-Diffuse to real life data, where SSVS-Diffuse out-performed the existing methods based on historical performance.