Family of High-Ordered Integer-Valued Auto-Regressive Models and Applications

This book tackles the complexities of integer-valued time series analysis, focusing on over-dispersion, excess zeros, and non-stationarity. It explores high-ordered INAR(p) models with diverse thinning mechanisms and innovation distributions, finding CML superior for inference. Addressing periodic-ity, harmonic functions are introduced for COVID-19 data. Novel BINAR (1) models with BPWE and SPWE innovations are applied to stock transactions, while new BPGL and SPGL bivariate distributions analyze crime data.

The book derives methodologies, tests performance via simulation, and provides real-life applications, filling a gap in existing literature. This comprehensive work significantly advances the field of integer-valued time series analysis by addressing key challenges such as over-dispersion and periodicity. The detailed exploration of high-ordered INAR(p) models under various thinning mechanisms and innovation distributions provides valuable insights into their performance, with the clear outperformance of the CML inferential method offering practical guidance for researchers. The innovative incorporation of harmonic functions to model the periodic nature of the COVID-19 data in Mauritius demonstrates a crucial adaptation to real-world phenomena. Furthermore, the development and application of novel BINAR (1) models and bivariate distributions like BPGL and SPGL expand the analytical toolkit for understanding the relationships between multiple integer-valued series, exemplified by their application to stock transactions and crime data. By deriving new methodologies, rigorously testing their performance through simulation, and illustrating their utility with diverse real-life applications, this book offers substantial theoretical and practical contributions to the field, addressing limitations in existing literature.

The target audience includes researchers, statisticians, and practitioners working with count data and time series analysis in fields like econometrics, finance, epidemiology, and criminology.

Ashwinee Devi Soobhug works as a Statistician/Senior Statistician at Statistics Mauritius She is affiliated with the Ministry of Finance, Economic Planning and Development in Port Louis, Mauritius. She is a prominent academic researcher known for her significant contributions to the fields of statistics and public health.

Naushad Mamode Khan is an Associate Professor in Statistics, at the University of Mauritius. His research interests are statistical modelling and computing applied to integer-valued time series modelling.

Sunecher Yuvraj is a Senior Lecturer of Finance and Statistics of the University of Technology Mauritius since 2011. He received his Post Doctorate in Statistical Modelling from the University of Bahia, Ph.D in Statistics from the University of Mauritius, Master in Business Administration from the Management College of South Africa, Master in Financial Economics and Degree in Mathematics from the University of Mauritius.