ASYMPTOTIC INFERENCE FOR UNIT ROOT PROCESSES WITH GARCH(1,1) ERRORS

Shiqing Ling · W.K. Li

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Abstract

This paper investigates the so-called one-step local quasi–maximum likelihood estimator for the unit root process with GARCH(1,1) errors. When the scaled conditional errors (the ratio of the disturbance to the conditional standard deviation) follow a symmetric distribution, the asymptotic distribution of the estimated unit root is derived only under the second-order moment condition. It is shown that this distribution is a functional of a bivariate Brownian motion as in Ling and Li (1998, Annals of Statistics 26, 84–125) and can be used to construct the unit root test.The authors thank the co-editor, Bruce Hansen, and two referees for very helpful comments and suggestions. W.K. Li's research is partially supported by the Hong Kong Research Grants Council. Ling's research is supported by RGC Competitive Earmarked Research grant HKUST6113/02P.

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References

1986Generalized autoregressive conditional heteroskedasticity 1987Time Series Regression with a Unit Root 1990Stationarity and Persistence in the GARCH(1,1) Model 1986Multiple Time Series Regression with Integrated Processes 1994Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator 1991Weak Limit Theorems for Stochastic Integrals and Stochastic Differential Equations 1996Consistency and Asymptotic Normality of the Quasi-Maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models 1997On Fractionally Integrated Autoregressive Moving-Average Time Series Models With Conditional Heteroscedasticity

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