Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator
- 1 March 1994
- journal article
- research article
- Published by Cambridge University Press (CUP) in Econometric Theory
- Vol. 10 (1), 29-52
- https://doi.org/10.1017/s0266466600008215
Abstract
This paper investigates the sampling behavior of the quasi-maximum likelihood estimator of the Gaussian GARCH(1,1) model. The rescaled variable (the ratio of the disturbance to the conditional standard deviation) is not required to be Gaussian nor independent over time, in contrast to the current literature. The GARCH process may be integrated (α + β = 1), or even mildly explosive (α + β > 1). A bounded conditional fourth moment of the rescaled variable is sufficient for the results. Consistent estimation and asymptotic normality are demonstrated, as well as consistent estimation of the asymptotic covariance matrix.Keywords
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