The performance of conditional heteroskedastic VAR enhanced Multivariate GARCH models on the time varying integrated data

Abstract

The study investigated the performance of conditional heteroskedastic vector autoregressive (VAR) enhanced Multivariate GARCH models on the time varying integrated data. These models allow the conditional-on-past-history covariance matrix of the dependent variables to follow a flexible dynamic structure. The study evaluated the levels of interdependence and dynamic linkage among the BRICS financial markets (in particular exchange rates) using appropriate univariate and multivariate time-series models. The study employed the monthly time series data of the BRICS exchange rates ranging from January 2008 to January 2018 and it has 121 observations. The base model used in the study was a VAR model, an ARCH model was fitted with the effects the model presented. Subsequently an extension of ARCH model, which is GARCH, was considered together with its multivariate settings. The focus of the study was to estimate the VAR enhanced Multivariate GARCH using the BEKK and DCC approach on the BRICS exchange rates. The study took a guide from some studies as presented in the literature. All the statistical properties necessary to test prior to engaging further with the analysis were satisfied. The VAR (1) model was fitted and the parameters were estimated. The results revealed that a linear dependency between the BRICS exchange rates existed. All the linear dependencies took one direction. The squared BRICS exchange rates illustrated the presence of serial correlation and that the ARCH errors were present in the BRICS exchange rates. The LM test for the ARCH model strongly showed the presence of heteroskedasticity of errors for GARCH model for the five countries. The univariate GARCH (1.1), EGARCH (1.1) and TGARCH (1.1) models for the BRICS exchange rates were fitted to the data and all followed a normal distribution. All the three models were fitted using Student t-distribution (std). The GARCH (1.1) model found the unconditional volatility for each of the BRICS exchange rates series. EGARCH (1.1) and TGARCH (1.1) models on the other hand presented the leverage effect. The EGARCH (1.1) model illustrated that the asymmetric effects dominate the symmetric effects except for South Africa as opposed to the TGARCH (1.1) model where the symmetric effects dominates the asymmetric effects. The

estimated leverage effect ) for all the BRICS exchange rates proved that the bad news has no effect to the volatility as compared to the remaining BRICS exchange rates. Multivariate GARCH using the BEKK estimates of the diagonal parameters showed that only Russia and South Africa were statistically significant which implied that the conditional variance of Russia and South Africa’s exchange rates are affected by their own past conditional volatility and other BRICS exchange rates past conditional volatility. On the other hand, VAR enhanced Multivariate GARCH using the BEKK estimates of the diagonal parameters, showed that only the conditional variance of Brazil, China, India and Russia’s exchange rates are affected by their own past conditional volatility and other BRICS exchange rates past conditional volatility. Both methods revealed that there are no spill-over effects in the BRICS exchange rates. The negative impact each of the BRICS exchange rates had did not affect other BRICS exchange rates. The BEKK-GARCH revealed that only one pair (Russia and South Africa) had a bidirectional volatility transmission whereas on the VAR enhanced BEKK-GARCH did not reveal any bidirectional volatility transmission between the BRICS exchange rates. The BEKK-GARCH model demonstrated the presence of autocorrelation in the residuals while the VAR enhanced BEKK-GARCH model demonstrated the absence of the autocorrelation in the residuals. This implied that the VAR enhanced BEKK-GARCH model was well specified. The DCC-GARCH model did not follow a normal distribution whereas the VAR enhanced DCC GARCH model follows a normal distribution with some extreme tails. Moreover, the DCC-GARCH revealed that Brazil, China, Russia and South Africa had the highest volatility persistence and India had the least volatility persistence as opposed to the VAR enhanced DCC-GARCH model which revealed that India had the highest volatility persistence followed by Brazil, Russia and South Africa and China with the least volatility persistence. The study contributes to the knowledge base the fresh discussion on the performance of Multivariate GARCH processes and the assessment of the performance of the conditional heteroskedastic VAR enhanced Multivariate GARCH model on the time varying integrated data. Recommendations for further studies were also provided.