Abstract
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 by Thavaneswaran 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.
Highlights
There has been growing interest in using nonlinear time series models in finance and economics
By analogy with the Random coefficient autoregressive (RCA) models we introduce a class of RCA versions of the GARCH models
Applications In Thavaneswaran et al [21], we have studied the volatility forecasting for zero mean GARCH processes and derived the forecast error variance in terms of GARCH kurtosis
Summary
There has been growing interest in using nonlinear time series models in finance and economics (see Granger [13], He and Terasvirta [15] and Heston [16] including others). A nonlinear model had been proposed by Abraham and Thavaneswaran [1] and using nonlinear state space formulation, filtering, and smoothing had been studied (see Granger [13] for more details) Many financial series, such as returns on stocks and foreign exchange rates, exhibit leptokurtosis and time-varying volatility. He and Terasvirta [15] and Heston [16] examined the forth moment structure of the GARCH(1,1) model with conditionally nonnormal innovations and they extended their results to the GARCH(p, q) model.
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