Hierarchical Semi-parametric Duration Models

Abstract: 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.