Asymptotic normality of the QMLE of possibly nonstationary GARCH with serially dependent innovations∗

This paper proposes a new parametric volatility model that introduces serially dependent innovations in GARCH specifications. We first prove the asymptotic normality of the QML estimator in this setting, allowing for possible explosive and nonstationary behavior of the GARCH process. We show that this model can generate an alternative measure of risk premium relative to the GARCH-M. Finally, we provide evidence of the usefulness and advantages of our approach relative to competing volatility models through a Monte Carlo experiment and by an application to US treasury bill spot rates. In particular, we illustrate the consequences of dynamic misspecification and demonstrate that the new volatility model can improve upon the fit in-sample as well as out-of-sample relative to traditional GARCH-type specifications.