PoARX Modelling for Multivariate Count Time Series

TL;DR

This paper develops multivariate PoARX models for count time series, establishing their statistical properties, proposing efficient estimation methods, and demonstrating their predictive power through a building entry-exit dataset.

Contribution

It introduces PoARX models with conditions for stationarity and ergodicity, along with a computationally efficient estimation procedure and asymptotic properties.

Findings

Model accurately predicts building entry-exit counts

Estimation method is computationally efficient

Model demonstrates strong predictive performance

Abstract

This paper introduces multivariate Poisson autoregressive models with exogenous covariates (PoARX) for modelling multivariate time series of counts. We obtain conditions for the PoARX process to be stationary and ergodic before proposing a computationally efficient procedure for estimation of parameters by the method of inference functions (IFM) and obtaining asymptotic normality of these estimators. Lastly, we demonstrate an application to count data for the number of people entering and exiting a building, and show how the different aspects of the model combine to produce a strong predictive model. We conclude by suggesting some further areas of application and by listing directions for future work.