GARCH for Irregularly Spaced Financial Data: The ACD-GARCH Model

We develop a class of ARCH models for series sampled at unequal time intervals set by trade or quote arrivals. Our approach combines insights from the temporal aggregation for GARCH models discussed by Drost and Nijman (1993) and Drost and Werker (1996), and the autoregressive conditional duration model of Engle and Russell (1996) proposed to model the spacing between consecutive financial transactions. The class of models introduced here will be called ACD-GARCH. It can be described as a random coefficient GARCH, or doubly stochastic GARCH, where the durations between transactions determine the parameter dynamics. The ACD-GARCH model becomes genuinely bivariate when past asset-return volatilities are allowed to affect transaction durations, and vice versa. Otherwise, the spacings between trades are considered exogenous to the volatility dynamics. This assumption is required in a two-step estimation procedure. The bivariate setup enables us to test for Granger causality between volatility and intratrade durations. Under general conditions, we propose several Generalized Method of Moments (GMM) estimation procedures, some having a Quasi Maximum Likelihood Estimation (QMLE) interpretation. As illustration, we present an empirical study of the IBM 1993 tick-by-tick data. We find some evidence that volatility of IBM stock prices Granger-causes intratrade durations. We also find that the persistence in GARCH drops dramatically once intratrade durations are taken into account.

Ghysels E. and Jasiak J. (1998) GARCH for Irregularly Spaced Financial Data: The ACD-GARCH Model. Studies in Nonlinear Dynamics and Econometrics, 2.