Simulation study on the in-sample forecasting performances of Sims-Zha Bayesian VARX in the presence of collinearity between the exogenous variables for small sample situation

In time series literature, exogenous variables tend to improve the forecast of the endogenous variables. This paper examined the forecast performance of six (6) versions of Bayesian Vector Autoregressive models with exogenous variables (BVARX) using normal-inverse Wishart Prior when collinearity exist between the exogenous variables for small sample situations. To achieve this, VAR(2) model was used to simulate bivariate time series from a stable process while bivariate exogenous variables were simulated from a standard normal distribution to possess the following collinearity levels: -0.99, -0.95, -0.9, -0.85, -0.8, 0.8, 0.85, 0.9, 0.95, 0.99. The experiment was carried out in R environment and repeated 10,000 times for the following time series lengths: 8, 16, 32 and 50. The Root Mean Square Error (RMSE) and the Mean Absolute Error (MAE) were used to adjudge the models. In all the scenarios considered, BVARX4 performed best while BVARX1 performed worst in all the collinearity levels and time series lengths. Lastly, RMSE and MAE values of the BVARX models are higher with negative collinearity compared to positive collinearity while the values of RMSE and MAE for the BVARX model decreased as the time series length increased. 

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