Doukhan, Paul Probabilistic and statistical tools for modeling time series. Paper from the 30th Brazilian mathematics colloquium – 30\(^{\text o}\) Colóquio Brasileiro de Matemática, Rio de Janeiro, Brazil, July 26–31, 2015. (English) Zbl 1335.62006 Publicações Matemáticas do IMPA. Rio de Janeiro: Instituto Nacional de Matemática Pura e Aplicada (IMPA) (ISBN 978-85-244-0411-5/pbk). 272 p., open access (2015). This is a text for a short course at the 30th Brazilian Colloquium of Mathematics, held at IMPA, Rio de Janeiro. The text contains three parts, each with four chapters. Part I, “Independence and stationarity”, has chapters on “Independence”, “Gaussian convergence and moments”, “Estimation concepts” and “Stationarity”. Part II, “Models of time series”, includes chapters on “Gaussian chaos”, “Linear models”, “Nonlinear models” and “Association”. Finally, Part III, on “Dependences”, includes chapters on “Ergodic theorem”, “Long range dependence”, “Short range dependence” and “Moment methods”. There are also three appendices, on “Probability”, “Distributions” and “Limit theory”. As indicated by the author, the purpose of the lectures is introductory, eventhough at an advanced level. Reviewer: Pedro A. Morettin (São Paulo) MSC: 62-06 Proceedings, conferences, collections, etc. pertaining to statistics 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 60-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory 60G10 Stationary stochastic processes 60G15 Gaussian processes 62Fxx Parametric inference Keywords:time series; probabilistic tools; statistical tools; modelling PDFBibTeX XMLCite \textit{P. Doukhan}, Probabilistic and statistical tools for modeling time series. Paper from the 30th Brazilian mathematics colloquium -- 30\(^{\text o}\) Colóquio Brasileiro de Matemática, Rio de Janeiro, Brazil, July 26--31, 2015. Rio de Janeiro: Instituto Nacional de Matemática Pura e Aplicada (IMPA) (2015; Zbl 1335.62006) Full Text: Link