There are some evidences of autocorrelation and heteroscedasticity in the returns of India VIX, hence in the empirical model an AR term has been added to resolve the autocorrelation problem, and the resulted residuals are modelled in ARCH/ GARCH
framework to control the heteroscedasticity.
These methods can be applied directly to the return series, but since we have observed significant GARCH
effects it would be desirable to pre-filter the return series with a GARCH
model to be able to accommodate for suddenly increasing or decreasing volatility.
We then perform the linear and nonlinear Granger tests again using the GARCH
In order to incorporate conditional heteroskedasticity, usually present in the indexes of stock markets, variance-covariance matrixes are estimated, using various multivariate GARCH
models, namely the VECH, BEKK and CCC models, whose theoretical assumptions are presented in the following section.
The first equation (eq 1), specify the conditional mean equation of GARCH
9) The Appendix Table A1 and Figure A1 depict the significant volatility measure from GARCH
in industrial energy consumption.
2005), by using a Bivariate GARCH
(BGARCH) model, find that inflation uncertainty decreased inflation and output growth for the US, but output uncertainty increased growth but reduced inflation.
This insures high forecast accuracy because the majority of studies report that GARCH
forecast accuracy increases as the length of the in-sample period increases (see, for example, Figlewski  and Brownlees et al.
The null of no GARCH
effects is clearly rejected for both cases thus confirming the importance of modeling the volatility of the time series and validating the role played by volatility in capturing the rate of information flow.
For roundwood export volume, exchange rate volatility shows a negative impact in the short-run but it is only significant with the GARCH
measure in the VECM model.
However, as there are many forms of non-linearity, which are also specific to the particular stock market data used, finding an optimal GARCH
specification is not a trivial task.
models and Financial Crisis--A study of Malayasian Stock market.