Flexible bivariate INGARCH process with a broad range of contemporaneous correlation

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 the finite-sample behavior of the estimators is investigated through simulation studies. Asymptotic properties of the CML estimators are derived. Hypothesis testing methods for the presence of contemporaneous correlation between the time series are presented and evaluated. A Granger causality test is also addressed. We apply our methodology to monthly counts of hepatitis cases in 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.