Stochastic Models for Time Series

Paul Doukhan is a Professor at the University of Cergy-Pontoise, Paris. He is an established researcher in the area of non-linear time series. Chiefly focusing on the dependence of stochastic processes, he has published a large number of methodological research papers and authored several books in this research area.

“We are dealing with a monograph that compiles a broad set of fundamental results on the probabilistic and statistical analysis of time series, and is mathematically rigorous and effectively suitable to support theoretical and practical re-search in the general field of stochastic processes.” (Nazare Mendes Lopes, Mathematical Reviews, July, 2019)“Although there are several books written on time series and stochastic processes, this book is the first one to present stochastic modelling approaches in linear/nonlinear time series. … This book is intended for masters and higher undergraduate students in mathematics, probability, statistics, astrophysics, biomedical engineering, and neuroscience. However, the students who want to pursue a PhD in the modelling of non-linear time series should also read this book to gain fundamental background knowledge.” (Chitaranjan Mahapatra, ISCB News, iscb.info, Issue 67, June, 2019)“The book is well-written and mathematically rigorous. The author is certainly one of the best specialists in the field worldwide. He has collected a large variety of results. To date there is no book like this. It may become the standard reference for researchers working on the topic. In summary, this is a very useful book for a researcher in probability and stochastic processes, which can also be used for under- and post-graduate courses.” (Nikolai N. Leonenko, zbMATH 1401.62007, 2019)

• Part I Independence and Stationarity.- 1 Probability and Independence.- 2 Gaussian convergence and inequalities.- 3 Estimation concepts.- 4 Stationarity.- Part II Models of time series.- 5 Gaussian chaos.- 6 Linear processes.- 7 Non-linear processes.- 8 Associated processes.- Part III Dependence.- 9 Dependence.- 10 Long-range dependence.- 11 Short-range dependence.- 12 Moments and cumulants.- Appendices.- A Probability and distributions.- B Convergence and processes.- C R scripts used for the gures.- Index- List of figures.