摘要：In financial modeling, it has been constantly pointed out that
volatility clustering and conditional nonnormality induced leptokurtosis observed
in high frequency data. Financial time series data are not adequately
modeled by normal distribution, and empirical evidence on the non-normality
assumption is well documented in the financial literature (details are illustrated by Engle (1982) and Bollerslev (1986)). An ARMA representation has been used byThavaneswaran
et al., in 2005, to derive the kurtosis of the various class of GARCH
models such as power GARCH, non-Gaussian GARCH, nonstationary and
random coefficient GARCH. Several empirical studies have shown that mixture
distributions are more likely to capture heteroskedasticity observed in high frequency
data than normal distribution. In this paper, some results on moment
properties are generalized to stationary ARMA process with GARCH errors.
Application to volatility forecasts and option pricing are also discussed in some
detail.
