Flexible bivariate INGARCH process with a broad range of contemporaneous correlation

Luiza S.C. Piancastelli; Wagner Barreto-Souza; Hernando Ombao

doi:10.1111/jtsa.12663

Flexible bivariate INGARCH process with a broad range of contemporaneous correlation

Luiza S.C. Piancastelli, Wagner Barreto-Souza^*, Hernando Ombao

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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.

Original language	English (US)
Pages (from-to)	206-222
Number of pages	17
Journal	Journal of Time Series Analysis
Volume	44
Issue number	2
DOIs	https://doi.org/10.1111/jtsa.12663
State	Published - Mar 2023

Bibliographical note

Funding 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).

Publisher Copyright:
© 2022 John Wiley & Sons Ltd.

Keywords

asymptotics
cross-correlation
ergodicity
multivariate count time series
stability theory

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1111/jtsa.12663

Cite this

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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.",

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author = "Piancastelli, {Luiza S.C.} and Wagner Barreto-Souza and Hernando Ombao",

note = "Funding 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 Cient{\'i}fico e Tecnol{\'o}gico (CNPq‐Brazil, Grant number 305543/2018‐0). Publisher Copyright: {\textcopyright} 2022 John Wiley & Sons Ltd.",

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N2 - 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.

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Flexible bivariate INGARCH process with a broad range of contemporaneous correlation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

UN SDGs

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