  Engle and Russell (1998, Econometrica, 66:1127--1162) apply results from the
GARCH literature to prove consistency and asymptotic normality of the
(exponential) QMLE for the generalized autoregressive conditional duration
(ACD) model, the so-called ACD(1,1), under the assumption of strict
stationarity and ergodicity. The GARCH results, however, do not account for the
fact that the number of durations over a given observation period is random.
Thus, in contrast with Engle and Russell (1998), we show that strict
stationarity and ergodicity alone are not sufficient for consistency and
asymptotic normality, and provide additional sufficient conditions to account
for the random number of durations. In particular, we argue that the durations
need to satisfy the stronger requirement that they have finite mean.
