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.
Bibliographical noteFunding Information:
The authors thank the Associate Editor and two Referees for their constructive criticisms and comments that lead to an improvement of the paper. Luiza S. C. Piancastelli thanks the financial support of Science Foundation Ireland under Grant number 18/CRT/6049. Wagner Barreto‐Souza and Hernando Ombao acknowledge the financial support by KAUST Research Fund. Wagner Barreto‐Souza also thanks the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq‐Brazil, Grant number 305543/2018‐0).
© 2022 John Wiley & Sons Ltd.
- multivariate count time series
- stability theory
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics