Articlebronze2008

Normal Mixture Quasi‐maximum Likelihood Estimator for GARCH Models

26 citations0/0 files storedScandinavian Journal of Statistics

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Financial Risk and Volatility Modeling Stochastic processes and financial applications Bayesian Methods and Mixture Models

Abstract

Abstract. The generalized autoregressive conditional heteroscedastic (GARCH) model has been popular in the analysis of financial time series data with high volatility. Conventionally, the parameter estimation in GARCH models has been performed based on the Gaussian quasi‐maximum likelihood. However, when the innovation terms have either heavy‐tailed or skewed distributions, the quasi‐maximum likelihood estimator (QMLE) does not function well. In order to remedy this defect, we propose the normal mixture QMLE (NM‐QMLE), which is obtained from the normal mixture quasi‐likelihood, and demonstrate that the NM‐QMLE is consistent and asymptotically normal. Finally, we present simulation results and a real data analysis in order to illustrate our findings.

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References

1986Generalized autoregressive conditional heteroskedasticity 1992Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances 1987A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return 2000Stable Paretian Models in Finance 1994Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator 2004Maximum likelihood estimation of pure GARCH and ARMA-GARCH processes 1992Stationarity of Garch processes and of some nonnegative time series 1986Asymptotic Theory for ARCH Models: Estimation and Testing

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