In this paper we introduce an ACD-ECOGARCH(1,1) model. An exponential autoregressive conditional duration model is used to describe the dependence structure in durations of ultra-high-frequency financial data. The innovation process of the ACD model then defines the interarrival times of a compound Poisson process. We use this compound Poisson process as the background driving Lévy process of an exponential continuous time GARCH(1,1) process. The dynamics of the random time transformed log-price process are then described by the latter process. To estimate its parameters we construct a quasi maximum likelihood estimator under the assumption that all jumps of the log-price process are observable. Finally, the model is fitted for illustrative purpose to General Motors tick-by-tick data of the New York Stock Exchange.

KEYWORDS: ACD, ECOGARCH, leverage effect, QMLE, ultra-high-frequency data