Handbook of Discrete-valued Time Series
Safaa K. Kadhem · Journal of the Royal Statistical Society Series A (Statistics in Society) · 2017
Many textbooks aim to cover a range of statistical topics to engage researchers using such methods in a range of disciplines. This book is rather more specialized in its coverage of the modelling of different observed count-process-based time series and would be suitable for statistical researchers and graduate students. It is enhanced with a good number of interesting examples. The book consists of five main sections, each of which consists of several chapters. The first part of the book includes eight chapters modelling univariate count data time series. A wide range of approaches is included, such as state space, generalized linear auto-regressive moving average, integer-valued and observation-driven auto-regressive parameter dynamic models. Part II of the book, entitled ‘Diagnostics and applications’, includes three chapters. The first chapter in this part focuses on the adequacy and assessment of many count data time series models. The authors introduce a range of diagnostic tools such as scoring rules, dedicated statistical tests and graphical diagnostics. The second chapter in this part concerns change point detection for a class of integer-valued time series models using diagnostic tools such as exponentially weighted moving averages and cumulative sums. The final chapter in this section concerns Bayesian estimation using sequential filtering methods (an attractive alternative to Markov chain Monte Carlo sampling) for a class of Poisson time series fitted to count data for several business applications involving marketing and finance. Part III contains three chapters on state space time series models for count data such as hidden Markov models, qualitative values time series models and binary time series. Finally, part IV consists of four chapters which discuss Bayesian hierarchical modelling for discrete-valued spatiotemporal data. These include generalized linear mixed models, so-called agent-based models and autologistic regression in the first three chapters. The fourth chapter of this section introduces a survey of the most commonly used descriptive models for spatiotemporal time series. This final chapter was supported by application areas involving disease and surveillance data. One important issue is model selection. According to the contents, the authors have specified a full section related to this topic (part II). Nevertheless, many other chapters could have provided more information on this issue. That said, Chapters 9, 12 and 14 did address tools such as the Akaike information criterion and the Bayesian information criterion. However, the use of such traditional tools for model selection should be quite familiar to many and I feel that more attention could be given to newer and more efficient criteria. I also believe that more attention could be given to intricacies of model fit in different ways. We also feel from an organizational viewpoint that the book could have been organized differently: the split into five sections perhaps undermines the core ideas of latent variables and especially state space models that are so well presented here. Generally, the book includes theoretical derivations and formulae that have been written in a readily understood and simple way and it makes it easy for the reader to follow the corresponding applications. Nevertheless, it does assumes some familiarity with the application topics. Overall, this is a good authoritative source. The authors have gathered material within specific topics to make it a useful and easy reference for researchers who are interested in count data time series. This book is aimed at postgraduate students and it can be used as a research source.