Improvement of Vector Autoregression (VAR) estimation using Combine White Noise (CWN) technique

Previous studies revealed that Exponential Generalized Autoregressive Conditional Heteroscedastic (EGARCH) outperformed Vector Autoregression (VAR) when data exhibit heteroscedasticity. However, EGARCH estimation is not efficient when the data have leverage effect. Therefore, in this study the weaknesses of VAR and EGARCH were modelled using Combine White Noise (CWN). The CWN model was developed by integrating the white noise of VAR with EGARCH using Bayesian Model Averaging (BMA) for the improvement of VAR estimation. First, the
standardized residuals of EGARCH errors (heteroscedastic variance) were decomposed into equal variances and defined as white noise series. Next, this series was transformed into CWN model through BMA. The CWN was validated using comparison study based on simulation and four countries real data sets of Gross Domestic Product (GDP). The data were simulated by incorporating three sample sizes with low, moderate and high values of leverages and skewness. The CWN model was compared with three existing models (VAR, EGARCH and Moving Average (MA)). Standard error, log-likelihood, information criteria and forecast error measures were used to evaluate the performance of the models. The simulation findings showed that
CWN outperformed the three models when using sample size of 200 with high leverage and moderate skewness. Similar results were obtained for the real data sets where CWN outperformed the three models with high leverage and moderate
skewness using France GDP. The CWN also outperformed the three models when using the other three countries GDP data sets. The CWN was the most accurate model of about 70 percent as compared with VAR, EGARCH and MA models. These
simulated and real data findings indicate that CWN are more accurate and provide better alternative to model heteroscedastic data with leverage effect.