Extreme value theory for a class of EGARCH processes is developed. It is shown that the EGARCH process as well as the logarithm of its conditional variance lie in the domain of attraction of the Gumbel distribution. Norming constants are obtained and it is shown that the considered processes...

This paper is concerned with efficient GMM estimation and inference in GARCH models. Sufficient conditions for the estimator to be consistent and asymptotically normal are established for the GARCH(1,1) conditional variance process. In addition efficiency results are obtained in the general...

This paper considers adaptive estimation in nonstationary autoregressive moving average models with the noise sequence satisfying a generalised autoregressive conditional heteroscedastic process. The locally asymptotic quadratic form of the log-likelihood ratio for the model is obtained. It is...