Realized GARCH: A Complete Model of Returns and Realized Measures of Volatility

GARCH models have been successful in modeling financial returns. Still, much is to be gained by incorporating a realized measure of volatility in these models. In this paper we introduce a new framework for the joint modeling of returns and realized measures of volatility. The Realized GARCH framework nests most GARCH models as special cases and is, in many ways, a natural extension of standard GARCH models. We pay special attention to linear and log-linear Realized GARCH specifications. This class of models has several attractive features. It retains the simplicity and tractability of the classical GARCH framework; it implies an ARMA structure for the conditional variance and realized measures of volatility; and models in this class are parsimonious and simple to estimate. A key feature of the Realized GARCH framework is a measurement equation that relates the observed realized measure to latent volatility. This equation facilitates a simple modeling of the dependence between returns and future volatility that is commonly referred to as the leverage effect. An empirical application with DJIA stocks and an exchange traded index fund shows that a simple Realized GARCH structure leads to substantial improvements in the empirical fit over to the standard GARCH model. This is true in-sample as well as out-of-sample. Moreover, the point estimates are remarkably similar across the different time series.