Censored EM algorithm for Weibull mixtures: application to arrival times of market orders

TL;DR

This paper introduces a censored EM algorithm to analyze mixture distributions involving Weibull models, effectively capturing zero-inflated data in high-frequency trading order arrival times.

Contribution

It develops a novel censored EM algorithm tailored for Weibull mixture models, addressing zero-inflation in high-frequency trading data.

Findings

Successfully modeled zero-inflated order arrival times.

Applied method to four stocks on the London Stock Exchange.

Improved understanding of inter-arrival time distributions.

Abstract

In a previous analysis the problem of "zero-inflated" time data (caused by high frequency trading in the electronic order book) was handled by left-truncating the inter-arrival times. We demonstrated, using rigorous statistical methods, that the Weibull distribution describes the corresponding stochastic dynamics for all inter-arrival time differences except in the region near zero. However, since the truncated Weibull distribution was not able to describe the huge "zero-inflated" probability mass in the neighbourhood of zero (making up approximately 50\% of the data for limit orders), it became clear that the entire probability distribution is a mixture distribution of which the Weibull distribution is a significant part. Here we use a censored EM algorithm to analyse data for the difference of the arrival times of market orders, which usually have a much lower percentage of zero inflation, for four selected stocks trading on the London Stock Exchange.