GARCH FOR IRREGULARLY SPACED FINANCIAL DATA - THE ACD-GARCH MODEL

We develop a class of ARCH models for series sampled at unequal time i ntervals set by trade or quote arrivals. Our approach combines insight s from the temporal aggregation for GARCH models discussed by Drost an d Nijman (1993) and Drost and Werker (1996), and the autoregressive co nditional 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 a s a random coefficient GARCH, or doubly stochastic GARCH, where the du rations between transactions determine the parameter dynamics. The ACD -GARCH model becomes genuinely bivariate when past asset-return volati lities are allowed to affect transaction durations, and vice versa. Ot herwise, the spacings between trades are considered exogenous to the v olatility dynamics. This assumption is required in a two-step estimati on procedure. The bivariate setup enables us to test for Granger causa lity between volatility and intratrade durations. Under general condit ions, we propose several Generalized Method of Moments (GMM) estimatio n 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 tha t the persistence in GARCH drops dramatically once intratrade duration s are taken into account.