Flexible Bivariate INGARCH Process With a Broad Range of Contemporaneous Correlation

TL;DR

This paper introduces a flexible bivariate INGARCH model for count time series that can capture a wide range of contemporaneous correlations, with proven properties, estimation methods, and real-world application to hepatitis case data.

Contribution

The paper presents a novel BCP-INGARCH model capable of modeling both negative and positive correlations, along with theoretical properties, estimation techniques, and hypothesis testing methods.

Findings

Model effectively captures broad correlation range

Simulation studies validate estimator properties

Application to hepatitis data shows practical relevance

Abstract

We propose a novel flexible bivariate conditional Poisson (BCP) INteger-valued Generalized AutoRegressive Conditional Heteroscedastic (INGARCH) model for correlated count time series data. Our proposed BCP-INGARCH model is mathematically tractable and has as the main advantage over existing bivariate INGARCH models its ability to capture a broad range (both negative and positive) of contemporaneous cross-correlation which is a non-trivial advancement. Properties of stationarity and ergodicity for the BCP-INGARCH process are developed. Estimation of the parameters is performed through conditional maximum likelihood (CML) and finite sample behavior of the estimators are investigated through simulation studies. Asymptotic properties of the CML estimators are derived. Additional simulation studies compare and contrast methods of obtaining standard errors of the parameter estimates, where a bootstrap option is demonstrated to be advantageous. Hypothesis testing methods for the presence of contemporaneous correlation between the time series are presented and evaluated. We apply our methodology to monthly counts of hepatitis cases at two nearby Brazilian cities, which are highly cross-correlated. The data analysis demonstrates the importance of considering a bivariate model allowing for a wide range of contemporaneous correlation in real-life applications.