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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.

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
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