Time Series: a first course with Bootstrap Starter
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton ; London ; New York
CRC Press
[2020]
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| Series: | Texts in statistical science
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis: Seite 541-545 |
| Physical Description: | xix, 566 Seiten Diagramme 24 cm |
| ISBN: | 9781439876510 |
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Record in the Search Index
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| adam_text | Contents Preface xiii 1 Introduction 1.1 Time Series Data ............................................................................ 1.2 Cycles in Time Series Data............................................................. 1.3 Spanning and Scaling Time Series................................................. 1.4 Time Series Regression and Autoregression.................................. 1.5 Overview........................................................................................... 1.6 Exercises........................................................................................... 2 The 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 1 1 5 8 11 16 18 Probabilistic Structure of Time Series 25 Random Vectors............................................................................... 25 Time Series and Stochastic Processes........................................... 29 Marginals and Strict Stationarity ................................................. 32 Autocovariance and Weak Stationarity........................................ 35 Illustrations of Stochastic Processes.............................................. 40 Three Examples of White Noise.................................................... 44 Overview............................................................................................ 46 Exercises........................................................................................... 47 3 Trends, Seasonality, and Filtering 3.1 Nonparametric Smoothing........................... 3.2 Linear Filters and Linear Time
Series........................................... 3.3 Some Common Types of Filters.............................. 3.4 Trends .............................................................................................. 3.5 Seasonality........................................................................................ 3.6 Trend and Seasonality Together.................................................... 3.7 Integrated Processes......................................................................... 3.8 Overview ............................................................................................ 3.9 Exercises........................................................................................... 53 53 56 58 62 69 76 80 84 86 4 The Geometry of Random Variables 4.1 Vector Space Geometry and Inner Products................................... 93 93 vii
CONTENTS viii 4.2 Լշ(ք2, P, J7): The Space of Random Variables with Finite Second Moment............................................................................................... 97 4.3 Hilbert Space Geometry [*]................................................... 98 4.4 Projection in Hilbert Space............ ................................................... 101 4.5 Prediction of Time Series................................................................... 104 4.6 Linear Prediction of Time Series....................................................... 108 4.7 Orthonormal Sets and Infinite Projection........................................Ill 4.8 Projection of Signals [*]...................................................................... 113 4.9 Overview...............................................................................................119 4.10 Exercises ............................................................................................... 120 5 ARMA Models with White NoiseResiduals 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 6 Time Series in the Frequency Domain 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 169 The Spectral Density......................................................................... 169 Filtering in the Frequency Domain.................................................... 175 Inverse Autocovariances............................................. 181 Spectral Representation of Toeplitz Covariance Matrices............ 185 Partial Autocorrelations...................................................................... 189 Application to Model
Identification................................................. 193 Overview...............................................................................................196 Exercises...............................................................................................197 7 The Spectral Representation [*] 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 129 Definition of the ARMA Recursion.................................................... 129 Difference Equations............................................................................ 132 Stationarity and Causality of the AR(1)...........................................137 Causality of ARMA Processes.......................................................... 140 Invertibility of ARMA Processes....................................................... 144 The Autocovariance Generating Function........................................147 Computing ARMA Autocovariances via the MA Representation . 152 Recursive Computation of ARMA Autocovariances..................... 155 Overview...............................................................................................159 Exercises...............................................................................................160 207 The Herglotz Theorem ...................................................................... 207 The Discrete Fourier Transform....................................................... 212 The Spectral Representation............................................................. 215 Optimal
Filtering............................................................................... 220 Kolmogorov’s Formula ...................................................................... 225 The Wold Decomposition................................................................... 229 Spectral Approximation and the Cepstrum.....................................232 Overview....................................................... ...................................237 Exercises............................................................................... ·. . . . 239
CONTENTS ix 8 Information and Entropy [*] 247 8.1 Introduction........................................................................................ 247 8.2 Events and Information Sets.............................................................251 8.3 Maximum Entropy Distributions....................................... 254 8.4 Entropy in Time Series......................................................................258 8.5 Markov Time Series................................................ 262 8.6 Modeling Time Series via Entropy................................................... 265 8.7 Relative Entropy and Kullback-Leibler Discrepancy .................. 268 8.8 Overview.............................................................................................. 271 8.9 Exercises.................................... 272 9 Statistical Estimation 279 9.1 Weak Correlation and Weak Dependence....................................... 279 9.2 The Sample Mean . ..................................... 281 9.3 CLT for Weakly Dependent Time Series [*] 286 9.4 Estimating Serial Correlation.............................................................288 9.5 The Sample Autocovariance .............................................................291 9.6 Spectral Means ..................................................................................295 9.7 Statistical Properties of the Periodogram....................................... 301 9.8 Spectral Density Estimation.............................................................306 9.9 Refinements of Spectral
Analysis.......................................................311 9.10 Overview........................... 316 9.11 Exercises.................................... 318 10 Fitting Time Series Models 325 10.1 MA Model Identification...................................................................325 10.2 EXP Model Identification [*].............................................................328 10.3 AR Model Identification ...................................................................331 10.4 Optimal Prediction Estimators..........................................................336 10.5 Relative Entropy Minimization..........................................................341 10.6 Computation of Optimal Predictors................................................ 345 10.7 Computation of the Gaussian Likelihood....................................... 349 10.8 Model Evaluation............................................. 354 10.9 Model Parsimony and Information Criteria.................................... 359 10.10 Model Comparisons....................................... 361 10.11 Iterative Forecasting............................................................................ 366 10.12Applications to Imputation and Signal Extraction ..................... 370 10.13 Overview.............................................................................................. 373 10.14 Exercises.............................................................................................. 376 11 Nonlinear Time Series Analysis 385 11.1 Types of
Nonlinearity............................................. 385 11.2 The Generalized Linear Process [*]....................................................389 11.3 The ARCH Model............................................................................... 392 11.4 The GARCH Model............................................................................ 396 11.5 The Bi-spectral Density......................................................................400
X CONTENTS 11.6 Volatility Filtering......................................................... 404 11.7 Overview.............................................................................................. 409 11.8 Exercises.......................................... 411 12 The Bootstrap 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 12.10 A Probability A.l A.2 A.3 A.4 A.5 A. 6 507 Convergence Topologies..................................................................... 507 Convergence Results for Random Variables .................................510 Asymptotic Distributions.................................................................. 514 Central Limit Theory for Time Series.............................................519 Exercises............................................................................................. 528 D Fourier Series D.l D.2 487 Data ................................................................................................... 487 Sampling Distributions............................................ 489 Estimation.......................................................................................... 491 Inference............................................................................................. 493 Confidence Intervals........................................................................... 495 Hypothesis Testing ........................................................................... 498 Exercises............................................................................................. 502 C Asymptotics C.l C.2 C.3 C.4
C.5 467 Probability Spaces.............................................................................. 467 Random Variables.............................................................................. 470 Expectation and Variance.................................................................. 474 Joint Distributions.............................................................................. 478 The Normal Distribution.................................................................. 482 Exercises............................................................................................. 483 В Mathematical Statistics B.l B.2 B.3 B.4 B.5 B.6 B.7 415 Sampling Distributions of Statistics.................................................415 Parameter Functionals and Monte Carlo ........................................418 The Plug-In Principle and the Bootstrap........................................423 Model-Based Bootstrap and Residuals..............................................427 Sieve Bootstraps.................................................................................. 433 Time Frequency Toggle Bootstrap....................................................439 Subsampling........................................................................................ 444 Block Bootstrap Methods................................................................... 450 Overview.............................................................................................. 458 Exercises...................................................... 460 529 Complex Random Variables
.................. .................................... : 529 Trigonometric Polynomials.................................................*. . . . 531
CONTENTS E xi Stieltjes Integration 535 E.l Deterministic Integration................................................................ 535 E.2 Stochastic Integration...................................................................... 538 Index 547
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| adam_txt |
Contents Preface xiii 1 Introduction 1.1 Time Series Data . 1.2 Cycles in Time Series Data. 1.3 Spanning and Scaling Time Series. 1.4 Time Series Regression and Autoregression. 1.5 Overview. 1.6 Exercises. 2 The 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 1 1 5 8 11 16 18 Probabilistic Structure of Time Series 25 Random Vectors. 25 Time Series and Stochastic Processes. 29 Marginals and Strict Stationarity . 32 Autocovariance and Weak Stationarity. 35 Illustrations of Stochastic Processes. 40 Three Examples of White Noise. 44 Overview. 46 Exercises. 47 3 Trends, Seasonality, and Filtering 3.1 Nonparametric Smoothing. 3.2 Linear Filters and Linear Time
Series. 3.3 Some Common Types of Filters. 3.4 Trends . 3.5 Seasonality. 3.6 Trend and Seasonality Together. 3.7 Integrated Processes. 3.8 Overview . 3.9 Exercises. 53 53 56 58 62 69 76 80 84 86 4 The Geometry of Random Variables 4.1 Vector Space Geometry and Inner Products. 93 93 vii
CONTENTS viii 4.2 Լշ(ք2, P, J7): The Space of Random Variables with Finite Second Moment. 97 4.3 Hilbert Space Geometry [*]. 98 4.4 Projection in Hilbert Space. . 101 4.5 Prediction of Time Series. 104 4.6 Linear Prediction of Time Series. 108 4.7 Orthonormal Sets and Infinite Projection.Ill 4.8 Projection of Signals [*]. 113 4.9 Overview.119 4.10 Exercises . 120 5 ARMA Models with White NoiseResiduals 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 6 Time Series in the Frequency Domain 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 169 The Spectral Density. 169 Filtering in the Frequency Domain. 175 Inverse Autocovariances. 181 Spectral Representation of Toeplitz Covariance Matrices. 185 Partial Autocorrelations. 189 Application to Model
Identification. 193 Overview.196 Exercises.197 7 The Spectral Representation [*] 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 129 Definition of the ARMA Recursion. 129 Difference Equations. 132 Stationarity and Causality of the AR(1).137 Causality of ARMA Processes. 140 Invertibility of ARMA Processes. 144 The Autocovariance Generating Function.147 Computing ARMA Autocovariances via the MA Representation . 152 Recursive Computation of ARMA Autocovariances. 155 Overview.159 Exercises.160 207 The Herglotz Theorem . 207 The Discrete Fourier Transform. 212 The Spectral Representation. 215 Optimal
Filtering. 220 Kolmogorov’s Formula . 225 The Wold Decomposition. 229 Spectral Approximation and the Cepstrum.232 Overview.'.237 Exercises. ·. . . . 239
CONTENTS ix 8 Information and Entropy [*] 247 8.1 Introduction. 247 8.2 Events and Information Sets.251 8.3 Maximum Entropy Distributions. 254 8.4 Entropy in Time Series.258 8.5 Markov Time Series. 262 8.6 Modeling Time Series via Entropy. 265 8.7 Relative Entropy and Kullback-Leibler Discrepancy . 268 8.8 Overview. 271 8.9 Exercises. 272 9 Statistical Estimation 279 9.1 Weak Correlation and Weak Dependence. 279 9.2 The Sample Mean . . 281 9.3 CLT for Weakly Dependent Time Series [*] 286 9.4 Estimating Serial Correlation.288 9.5 The Sample Autocovariance .291 9.6 Spectral Means .295 9.7 Statistical Properties of the Periodogram. 301 9.8 Spectral Density Estimation.306 9.9 Refinements of Spectral
Analysis.311 9.10 Overview. 316 9.11 Exercises. 318 10 Fitting Time Series Models 325 10.1 MA Model Identification.325 10.2 EXP Model Identification [*].328 10.3 AR Model Identification .331 10.4 Optimal Prediction Estimators.336 10.5 Relative Entropy Minimization.341 10.6 Computation of Optimal Predictors. 345 10.7 Computation of the Gaussian Likelihood. 349 10.8 Model Evaluation. 354 10.9 Model Parsimony and Information Criteria. 359 10.10 Model Comparisons. 361 10.11 Iterative Forecasting. 366 10.12Applications to Imputation and Signal Extraction . 370 10.13 Overview. 373 10.14 Exercises. 376 11 Nonlinear Time Series Analysis 385 11.1 Types of
Nonlinearity. 385 11.2 The Generalized Linear Process [*].389 11.3 The ARCH Model. 392 11.4 The GARCH Model. 396 11.5 The Bi-spectral Density.400
X CONTENTS 11.6 Volatility Filtering. 404 11.7 Overview. 409 11.8 Exercises. 411 12 The Bootstrap 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 12.10 A Probability A.l A.2 A.3 A.4 A.5 A. 6 507 Convergence Topologies. 507 Convergence Results for Random Variables .510 Asymptotic Distributions. 514 Central Limit Theory for Time Series.519 Exercises. 528 D Fourier Series D.l D.2 487 Data . 487 Sampling Distributions. 489 Estimation. 491 Inference. 493 Confidence Intervals. 495 Hypothesis Testing . 498 Exercises. 502 C Asymptotics C.l C.2 C.3 C.4
C.5 467 Probability Spaces. 467 Random Variables. 470 Expectation and Variance. 474 Joint Distributions. 478 The Normal Distribution. 482 Exercises. 483 В Mathematical Statistics B.l B.2 B.3 B.4 B.5 B.6 B.7 415 Sampling Distributions of Statistics.415 Parameter Functionals and Monte Carlo .418 The Plug-In Principle and the Bootstrap.423 Model-Based Bootstrap and Residuals.427 Sieve Bootstraps. 433 Time Frequency Toggle Bootstrap.439 Subsampling. 444 Block Bootstrap Methods. 450 Overview. 458 Exercises. 460 529 Complex Random Variables
. . : 529 Trigonometric Polynomials.*. . . . 531
CONTENTS E xi Stieltjes Integration 535 E.l Deterministic Integration. 535 E.2 Stochastic Integration. 538 Index 547 |
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| spelling | McElroy, Tucker Verfasser (DE-588)171887107 aut Time Series a first course with Bootstrap Starter Tucker S. McElroy and Dimitris N. Politis Boca Raton ; London ; New York CRC Press [2020] xix, 566 Seiten Diagramme 24 cm txt rdacontent n rdamedia nc rdacarrier Texts in statistical science Literaturverzeichnis: Seite 541-545 Bootstrap-Statistik (DE-588)4139168-8 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 s Bootstrap-Statistik (DE-588)4139168-8 s b DE-604 Politis, Dimitris N. Verfasser (DE-588)171528603 aut Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032050418&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | McElroy, Tucker Politis, Dimitris N. Time Series a first course with Bootstrap Starter Bootstrap-Statistik (DE-588)4139168-8 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| subject_GND | (DE-588)4139168-8 (DE-588)4067486-1 |
| title | Time Series a first course with Bootstrap Starter |
| title_auth | Time Series a first course with Bootstrap Starter |
| title_exact_search | Time Series a first course with Bootstrap Starter |
| title_exact_search_txtP | Time Series a first course with Bootstrap Starter |
| title_full | Time Series a first course with Bootstrap Starter Tucker S. McElroy and Dimitris N. Politis |
| title_fullStr | Time Series a first course with Bootstrap Starter Tucker S. McElroy and Dimitris N. Politis |
| title_full_unstemmed | Time Series a first course with Bootstrap Starter Tucker S. McElroy and Dimitris N. Politis |
| title_short | Time Series |
| title_sort | time series a first course with bootstrap starter |
| title_sub | a first course with Bootstrap Starter |
| topic | Bootstrap-Statistik (DE-588)4139168-8 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| topic_facet | Bootstrap-Statistik Zeitreihenanalyse |
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