This paper examines long-term dependence in times between trades on financial markets. The autocorrelation functions of several intertrade duration series show a slow, hyperbolic rate of decay typical for long memory processes. For example, a shock to times between trades of the Alcatel stock on the Paris Stock Exchange (SBF Paris Bourse) may persist in the transactions time for a long period of 1000 or 2000 ticks. With an average duration of 52 seconds between transactions this may amount to sixteen or thirty two hours in calendar time. This paper introduces a fractionally integrated autoregressive conditional duration (FIACD) model for intertrade duration series. It also examines transformed duration processes representing times between consecutive returns to states of null, positive or negative returns. This approach captures the relationship between the duration persistence and return dynamics. The times elapsed between returns to various states feature very similar autocorrelation patterns and do not possess the long memory property. The persistence in durations is also determined by the times spent within specific states of returns. The average visiting time is state dependent, features intraday variation and may be considered as an instantaneous measure of state persistence. The long memory patterns are examined in data on the Alcatel and IBM stocks traded on the SBF Paris Bourse and NYSE.
