Parametric Time‐Variation in the Unconditional Volatility: Estimation and Inference

ABSTRACT We propose modeling time‐variation in the unconditional volatility by augmenting the standard GARCH model by a deterministic time‐varying intercept. The model, called the additive time‐varying (ATV‐)GARCH model, can be interpreted as a reduced form of a model including covariates and can be derived from a multiplicative decomposition of volatility. It is globally nonstationary but can be locally approximated by a stationary GARCH process. We develop an asymptotic theory using the general theory of nonlinear locally stationary processes. As the main contribution of the paper, we obtain consistency and asymptotic normality of the quasi‐maximum likelihood estimator of the parameters of the ATV‐GARCH model under a moderate strengthening of the standard assumptions used in stationary GARCH models. An empirical application to Oracle Corporation stock returns demonstrates the usefulness of the model.