Random coefficient GARCH models

Both volatility clustering and conditional nonormality 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 |yt|δ are given in terms of ψ-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 are also derived.