Random coefficient mixture (RCM) GARCH models

In financial modelling, it has been constantly pointed out that volatility clustering and conditional nonnormality induced leptokurtosis are observed in high frequency data. Financial time series data are not adequately modelled by normal distribution and empirical evidence on the nonnormality assumption is well documented in the financial literature (see [1,2] for details). An ARMA representation has been used in [3] to derive the kurtosis of the various class of GARCH models such as power GARCH, non-Gaussian GARCH, and nonstationary and random coefficient GARCH. Several empirical studies have shown that mixture distributions are more likely to capture heteroscedasticity observed in high frequency data than normal distribution. This paper derives the moments for a class of hidden Markov models including Markov switching models under mixture distribution. ARCH-type bilinear models considered by Giraitis and Surgailis [4] with mixture errors are also discussed in some details.