Bivariate Integer-Valued Time Series Models: Bivariate Models

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.

Sunecher Yuvraj is currently appointed as Senior Lecturer of Statistics and Finance at the School of Business, Management and Finance at the University of Technology Mauritius since 2011. He received his Doctorate in Statistics from the University of Mauritius in 2018.

Mamode Khan Naushad is an Associate Professor in Statistics at the Faculty of Social Sciences and Humanities at the University of Mauritius. He was awarded his PhD in Statistics from the University of Mauritius in 2010.

Vandna Jowaheer is a Professor and Chair in Applied Statistics at the University of Mauritius, Mauritius. She is an elected member of International Statistical Institute and a fellow of the African academic network.