Random coefficient GARCH models

Both volatility clustering and conditional nonnormality can induce the leptokurtosis typically observed in financial data. An ARMA representation is used to derive the kurtosis of the various class of GARCH models such as power GARCH, non-Gaussian GARCH, nonstationary and random coefficient GARCH. Formula for autocorrelations of the power GARCH process vertical bar yt vertical bar(delta) are given in terms of psi-weights. The kurtosis is also derived for random coefficient GARCH, nonstationary GARCH with possibly nonnormal errors and for hidden Markov GARCH models. The theoretical autocorrelation functions for various GARCH(1,1) models axe also derived. (c) 2005 Elsevier Ltd. All rights reserved.