GARCH for Irregularly Spaced Data: The ACD-GARCH Model

Preprint
Publisher Website
Google Scholar
    • preprint
      • Published in RePEc
Abstract
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 (1994), and the autoregressive conditional duration model of Engle and Russell (1996) proposed to model the spacing between consecutive financial transactions. The class of models we introduce 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 intra-trade durations. Under general conditions we propose several GMM estimation procedures, some having a QMLE interpretation. As illustration we present an empirical study of the IBM 1993 tick-by-tick data. We find that volatility of IBM stock prices Granger causes intra-trade durations. We also find that the persistence in GARCH drops dramatically once intra-trade durations are taken into account. Nous développons une classe de modèles ARCH pour les séries temporelles échantillonnées à intervalles inégaux comme des observations liées à des transactions de marché. Notre approche est fondée sur la méthode d'aggrégation temporelle pour les modèles ARCH de Drost et Nijman (1993) et de Drost et Werker (1994), et d'autre part sur le modèle autorégressif des moyennes conditionnelles des durées entre les transactions financières de Engle et Russell (1996). La classe de modèles présentée ici est nommée ACD-GARCH. Ce type de modèles peut être défini comme un GARCH aux coefficients al
All Related Versions

This publication has 0 references indexed in Scilit: