Distributional analysis of empirical volatility in GARCH processes (Q947260)

This paper considers in econometrics frequently used conditionally heteroskedastic time series given by \(y_k=\sigma_k\varepsilon_k.\) The conditional variance \(\sigma_k\) is unknown, but its form is typically specified by means of recursive equations of the type GARCH(p,q). The main result of this paper is to obtain the limiting distributions for the differences between the special functionals of \(y_k^2\) and their counterparts corresponding to the right hand side of the GARCH equation. The proposed method is based on comparing the distributions of observed and implied volatilities. Some results of a numerical experiment for the case of a normal limiting distribution are given.