How to cite this paper: Adenomon, M.O., Michael, V.A. and Evans, O.P. (2016) On the Performances of Classical VAR and Sims-Zha Bayesian VAR Models in the Presence of Collinearity and Autocorrelated Error Terms. Open Journal of Statistics, 6, 96-132. http://dx. AbstractIn time series literature, many authors have found out that multicollinearity and autocorrelation usually afflict time series data. In this paper, we compare the performances of classical VAR and Sims-Zha Bayesian VAR models with quadratic decay on bivariate time series data jointly influenced by collinearity and autocorrelation. We simulate bivariate time series data for different collinearity levels (−0.99, −0.95, −0.9, −0.85, −0.8, 0.8, 0.85, 0.9, 0.95, 0.99) and autocorrelation levels (−0.99, −0.95, −0.9, −0.85, −0.8, 0.8, 0.85, 0.9, 0.95, 0.99) for time series length of 8, 16, 32, 64, 128, 256 respectively. The results from 10,000 simulations reveal that the models performance varies with the collinearity and autocorrelation levels, and with the time series lengths. In addition, the results reveal that the BVAR4 model is a viable model for forecasting. Therefore, we recommend that the levels of collinearity and autocorrelation, and the time series length should be considered in using an appropriate model for forecasting.

Forecasts can either be short term, medium term or long term. In this work, we consider short term forecast because of the problem of limited data or time series data that often encounter in time series analysis. This simulation study considers the performances of the classical VAR and Sims-Zha Bayesian VAR for short term series at different levels of collinearity and correlated error terms. The results from 10,000 iteration reveal that the BVAR models are excellent for time series length of T = 8 for all levels of collinearity while the classical VAR is effective for time series length of T = 16 for all collinearity levels except when ρ = −0.9 and ρ = −0.95. Therefore, we recommend that for effective short term forecasting, the time series length, forecasting horizon and the collinearity level should be considered.