An Exponential Chi-Squared QMLE for Log-GARCH Models Via the ARMA Representation

Estimation of log-GARCH models via the ARMA representation is attractive because it enables a vast amount of already established results in the ARMA literature. We propose an exponential Chi-squared QMLE for log-GARCH models via the ARMA representation. The advantage of the estimator is that it corresponds to the theoretically and empirically important case where the conditional error of the log-GARCH model is normal. We prove the consistency and asymptotic normality of the estimator, and show that, asymptotically, it is as efficient as the standard QMLE in the log-GARCH(1,1) case. We also verify and study our results in finite samples by Monte Carlo simulations. An empirical application illustrates the versatility and usefulness of the estimator.