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.

Table of Contents:
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.

About the Author :
Sunecher Yuvraj is a Senior Lecturer of Statistics and Finance in the Department of Accounting, Finance and Economics at the School of Business, Management and Finance at the University of Technology Mauritius. He earned a PhD in statistics at the University of Mauritius in 2018. Dr. Yuvraj’s research interests span modeling time series of counts, statistical modeling, computational statistics and longitudinal data analysis. He has published extensively in recognized international journals published by Springer, Taylor & Francis, Wiley, DeGruyter and MDPI. Dr. Yuvraj has contributed significantly to the literature by developing novel univariate and multivariate integer-valued auto-regressive and integer-valued moving average time series models of different orders, with applications in various socioeconomic issues. He is also involved in MPhil/PhD supervision of research students and has served as Editor and Reviewer for many journals in the field of computational modeling, financial modeling and finance. Dr. Yuvraj has successfully completed numerous research projects locally with societally impactful research. He has actively contributed to the dissemination of knowledge to the research community, industry and policymakers. Dr. Yuvraj has provided his services to the Ministry of Gender Equality and Family Welfare as Consultant for the preparation of a ten-year strategic plan for children. Dr. Yuvraj is the Vice-President of the Society of Statistics and Data Analytics in Mauritius and a Member of the International Statistical Institute, South African Statistical Association and the Australian Econometric Society. He has also served as Visiting Professor at several institutions, including Savitrabai Phule University of Pune, India; Ibn Zohr University of Agadir, Morocco; and Chhatrapati Shahu Institute of Business Education and Research (CSIBER) of Kohlapur, India. Naushad Mamode Khan is an Associate Professor in statistics in the Department of Economics and Statistics at the Faculty of Social Sciences and Humanities at the University of Mauritius. He is also currently the Head of the Department of Economics and Statistics at the University of Mauritius and also the President of the Society of Statistics and Data Analytics in Mauritius. He earned a PhD in statistics at the University of Mauritius in 2010, and his thesis focused on the development of statistical models for longitudinal count data. Dr. Khan’s research areas include statistical modeling, distribution theory, longitudinal count data analysis, computational statistics, spatial count data modeling and integer-valued time series modeling. His most popular research works in recent years encompasses the significant development in uni- and multivariate integer-valued auto-regressive time series models and its applications in various disciplines. Dr. Khan was elected as the academic editor of Plos One and has been actively publishing in renowned rated statistics journals by Taylor & Francis, Wiley, DeGruyter, Springer, Plos One, MDPI and Elsevier. He has several successfully completed local and international PhD and post-doc supervisions mainly in the field of time series modeling and has also offered his services as a PhD examiner at the University of Pretoria, South Africa. Dr. Khan has served as a Visiting Professor at several institutions, including the University of Shahrood, Iran; INSA Universite de Lyon, France; Savitrabai University of Pune, India; and the University of Agadir, Morocco. He was also nominated from 2015 to 2018 to the Statistics Board as the representative of the Vice-Chancellor of the University of Mauritius at Statistics Mauritius, under the aegis of the Ministry of Finance and Economic Development in Mauritius. Vandna Jowaheer is a Professor and Chair of Applied Statistics at the University of Mauritius, Mauritius. She is an elected Member of the International Statistical Institute and a Fellow of the African academic network. Dr. Jowaheer’s research expertise lies in developing statistical models and methods which can be applied to analyze cross-sectional, multivariate, time-series and longitudinal data structures. She has published numerous papers in reputed international journals in the areas of theoretical and applied statistics.