Bivariate Integer-Valued Time Series Models

Bivariate Models

Sunecher Yuvraj, Mamode Khan Naushad, Vandna Jowaheer

• Publisher: CRC Press
• Year: 2025
• eBook ISBN: 9781040325384
• Edition: 0
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

This book proposes some novel models based on the autoregressive and moving average structures under various distributional assumptions of the innovation series for analysing non-stationary bivariate time series of counts.

Time series of count responses are recorded for different correlated variables which may be marginally dispersed relative to their means, may exhibit different levels of dispersion and may be commonly influenced by one or more dynamic explanatory variables. Analysis of such type of bivariate time series data is quite challenging and the challenge mounts up further if these time series are non-stationary. This book proposes some bivariate models that allow for different levels of dispersion as well as non-stationarity. Specifically, BINAR(1) and BINMA(1) models under Poisson, NB and COM-Poisson innovations are constructed and tested. Another important contribution of this book is in developing a novel estimation procedure for estimating the parameters of the proposed BINAR(1) and BINMA(1) models. Hence, a new estimation approach based on the GQL is proposed. Monte-Carlo simulations are implemented to assess the performance of the GQL. In some simple cases of stationarity, we also compare the GQL with the other estimation techniques such as CMLE and FGLS.

This book is a useful resource for undergraduate students, postgraduate students, researchers and academics in the field of time series models.

Table of contents

• Cover Page
• Half-Title Page
• Title Page
• Copyright Page
• Contents
• Preface
• Acknowledgments
• Authors
• 1 Introduction
• 2 Constrained BINAR(1) Model with Correlated Poisson Innovations
• 3 Constrained BINMA(1) Model with Correlated Poisson Innovations
• 4 Unconstrained BINAR(1) Model with Poisson Innovations
• 5 Unconstrained BINMA(1) Model with Poisson Innovations
• 6 Constrained BINAR(1) Model with Correlated NB Innovations
• 7 Constrained BINMA(1) Model with Correlated NB Innovations
• 8 Unconstrained BINAR(1) Model with NB Innovations
• 9 Unconstrained BINMA(1) Model with NB Innovations
• 10 Constrained BINAR(1) Model with Correlated COM-Poisson Innovations
• 11 Constrained BINMA(1) Model with Correlated COM-Poisson Innovations
• 12 Unconstrained BINAR(1) Model with COM-Poisson Innovations
• 13 Unconstrained BINMA(1) Model with COM-Poisson Innovations
• 14 Conclusion and Future Directions
• Bibliography
• Index