LEADER 04320nam 22006855 450 001 9910300111103321 005 20250331124108.0 010 $a9783319769387 010 $a3319769383 024 7 $a10.1007/978-3-319-76938-7 035 $a(CKB)4100000003359499 035 $a(DE-He213)978-3-319-76938-7 035 $a(MiAaPQ)EBC6314079 035 $a(MiAaPQ)EBC5577719 035 $a(Au-PeEL)EBL5577719 035 $a(OCoLC)1066184537 035 $a(PPN)226696979 035 $a(EXLCZ)994100000003359499 100 $a20180417d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStochastic Models for Time Series /$fby Paul Doukhan 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (XX, 308 p. 29 illus., 10 illus. in color.) 225 1 $aMathématiques et Applications,$x2198-3275 ;$v80 311 08$a9783319769370 311 08$a3319769375 320 $aIncludes bibliographical references and index. 327 $aPart 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. 330 $aThis book presents essential tools for modelling non-linear time series. The first part of the book describes the main standard tools of probability and statistics that directly apply to the time series context to obtain a wide range of modelling possibilities. Functional estimation and bootstrap are discussed, and stationarity is reviewed. The second part describes a number of tools from Gaussian chaos and proposes a tour of linear time series models. It goes on to address nonlinearity from polynomial or chaotic models for which explicit expansions are available, then turns to Markov and non-Markov linear models and discusses Bernoulli shifts time series models. Finally, the volume focuses on the limit theory, starting with the ergodic theorem, which is seen as the first step for statistics of time series. It defines the distributional range to obtain generic tools for limit theory under long or short-range dependences (LRD/SRD) and explains examples of LRD behaviours. More general techniques (central limit theorems) are described under SRD; mixing and weak dependence are also reviewed. In closing, it describes moment techniques together with their relations to cumulant sums as well as an application to kernel type estimation.The appendix reviews basic probability theory facts and discusses useful laws stemming from the Gaussian laws as well as the basic principles of probability, and is completed by R-scripts used for the figures. Richly illustrated with examples and simulations, the book is recommended for advanced master courses for mathematicians just entering the field of time series, and statisticians who want more mathematical insights into the background of non-linear time series. . 410 0$aMathématiques et Applications,$x2198-3275 ;$v80 606 $aStatistics 606 $aProbabilities 606 $aEconometrics 606 $aDynamics 606 $aStatistical Theory and Methods 606 $aProbability Theory 606 $aEconometrics 606 $aDynamical Systems 615 0$aStatistics. 615 0$aProbabilities. 615 0$aEconometrics. 615 0$aDynamics. 615 14$aStatistical Theory and Methods. 615 24$aProbability Theory. 615 24$aEconometrics. 615 24$aDynamical Systems. 676 $a519.55 700 $aDoukhan$b Paul$4aut$4http://id.loc.gov/vocabulary/relators/aut$0441999 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300111103321 996 $aStochastic models for time series$91563778 997 $aUNINA