Modelling, simulation and inference for multivariate time series of counts

TL;DR

This paper introduces a novel continuous-time multivariate count process model using Lévy-driven trawl processes, enabling independent modeling of serial and cross-sectional dependence, with applications to high-frequency financial data.

Contribution

It develops a new modeling framework for multivariate count time series with infinitely divisible marginals, including simulation and inference methods, and applies it to financial order book data.

Findings

Successfully models dependence structures in high-frequency financial counts

Provides a stochastic simulation algorithm for the proposed process

Demonstrates the model's ability to capture short and long memory effects

Abstract

This article presents a new continuous-time modelling framework for multivariate time series of counts which have an infinitely divisible marginal distribution. The model is based on a mixed moving average process driven by L\'{e}vy noise - called a trawl process - where the serial correlation and the cross-sectional dependence are modelled independently of each other. Such processes can exhibit short or long memory. We derive a stochastic simulation algorithm and a statistical inference method for such processes. The new methodology is then applied to high frequency financial data, where we investigate the relationship between the number of limit order submissions and deletions in a limit order book.