  This research attempts to model the stochastic process of trades in a limit
order book market as a marked point process. We propose a semi-parametric model
for the conditional distribution given the past, attempting to capture the
effect of the recent past in a nonparametric way and the effect of the more
distant past using a parametric time series model. Our framework provides more
flexibility than the most commonly used family of models, known as
Autoregressive Conditional Duration (ACD), in terms of the shape of the density
of durations and in the form of dependence across time. We also propose an
online learning algorithm for intraday trends that vary from day to day. This
allows us both to do prediction of future trade times and to incorporate the
effects of additional explanatory variables. In this paper, we show that the
framework works better than the ACD family both in the sense of prediction
log-likelihood and according to various diagnostic tests using data from the
New York Stock Exchange. In general, the framework can be used both to estimate
the intensity of a point process, and to estimate a the joint density of a time
series.
