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We model the stochastic process of trades in a limit order book market as a marked point process. We propose a semiparametric 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. Our model includes for intraday trends that vary from day to day and allows us both to do prediction of future trade times and to incorporate the effects of additional explanatory variables. We compare and evaluate models based on out-of-sample performance. Joint work with Mingyu Tang.