Modeling Inter-Trade Durations in the Limit Order Market

Abstract

The ultra high frequency limit order book data have brought many challenges to statistical analysis. After a brief introduction to the limit order book (LOB) data and some of their stylized facts, we discuss empirical features of inter-trade durations in the LOB market. We argue the limitations of recent work that uses Markov-switching multifractal inter-trade duration (MSMD) models in the analysis of the LOB data, and propose extensions which replace the assumption of exponential distributions on errors by Weibull and Gamma distributions. We then analyze the LOB data of Google from January 8 to January 10 in 2014. Through the comparison of the in- and out-of-sample performances between the original and extended MSMDs, we find that the extended models fit data better than the original one.