Distributional analysis of empirical volatility in GARCH processes

Conditionally heteroskedastic time series given by yk=σkɛkyk=σkɛk are frequently used in econometrics. The conditional variance σk2 is defined by a parametric function of past observations and volatilities. Since several conditionally heteroskedastic time series models have been suggested in the literature, we want to test if a given model fits well the data. The method we propose in this paper is based on comparing the distributions of the observed and implied volatilities. Our results can be used to assess the validity of the GARCH(p,q)GARCH(p,q) model.