國立虎尾科技大學 |

Stochastic Models for Time Series

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Stochastic Models for Time Series/ by Paul Doukhan.
Author:	Doukhan, Paul.
Description:	XX, 308 p. 29 illus., 10 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Statistics . -
Online resource:	https://doi.org/10.1007/978-3-319-76938-7
ISBN:	9783319769387

Stochastic Models for Time Series
Doukhan, Paul.

Stochastic Models for Time Series[electronic resource] /by Paul Doukhan. - 1st ed. 2018. - XX, 308 p. 29 illus., 10 illus. in color.online resource. - Mathématiques et Applications,801154-483X ;. - Mathématiques et Applications,76.

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.

This 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. .

ISBN: 9783319769387

Standard No.: 10.1007/978-3-319-76938-7doiSubjects--Topical Terms:

1253516
Statistics .

LC Class. No.: QA276-280

Dewey Class. No.: 519.5

Stochastic Models for Time Series
LDR:03623nam a22003975i 4500 001 991778
003 DE-He213
005 20200704093733.0
007 cr nn 008mamaa
008 201225s2018 gw | s |||| 0|eng d
020 $a 9783319769387 $9 978-3-319-76938-7
024 7 $a 10.1007/978-3-319-76938-7 $2 doi
035 $a 978-3-319-76938-7
050 4 $a QA276-280
072 7 $a PBT $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
082 0 4 $a 519.5 $2 23
100 1 $a Doukhan, Paul. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1203932
245 1 0 $a Stochastic Models for Time Series $h [electronic resource] / $c by Paul Doukhan.
250 $a 1st ed. 2018.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2018.
300 $a XX, 308 p. 29 illus., 10 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Mathématiques et Applications, $x 1154-483X ; $v 80
505 0 $a 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.
520 $a This 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. .
650 0 $a Statistics . $3 1253516
650 0 $a Probabilities. $3 527847
650 0 $a Econometrics. $3 556981
650 0 $a Dynamics. $3 592238
650 0 $a Ergodic theory. $3 672355
650 1 4 $a Statistical Theory and Methods. $3 671396
650 2 4 $a Probability Theory and Stochastic Processes. $3 593945
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 671353
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319769370
776 0 8 $i Printed edition: $z 9783319769394
830 0 $a Mathématiques et Applications, $x 1154-483X ; $v 76 $3 1263208
856 4 0 $u https://doi.org/10.1007/978-3-319-76938-7
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)