Verfügbarkeit: Time series :: THWS Bibkatalog

Time series: theory and methods

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Bibliographische Detailangaben
Hauptverfasser:	Brockwell, Peter J. 1937-2023 (VerfasserIn), Davis, Richard A. 1952- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona Springer-Verlag [1991]
Ausgabe:	Second edition
Schriftenreihe:	Springer series in statistics
Schlagworte:	Série chronologique Tijdreeksen Time-series analysis Zeitreihenanalyse Lehrbuch
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	Hier auch später erschienene, unveränderte Nachdrucke
Beschreibung:	xvi, 577 Seiten Illustrationen
ISBN:	0387974296 3540974296 9781441903198 9781441903204

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Datensatz im Suchindex

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adam_text	Contents Preface to the Second Edition vii Preface to the First Edition ix CHAPTER 1 Stationary Time Series 1 §1.1 Examples of Time Series 1 §1.2 Stochastic Processes 8 §1.3 Stationarity and Strict Stationarity 11 §1.4 The Estimation and Elimination of Trend and Seasonal Components 14 §1.5 The Autocovariance Function of a Stationary Process 25 §1.6 The Multivariate Normal Distribution 32 §1.7* Applications of Kolmogorov's Theorem 37 Problems 39 CHAPTER 2 Hilbert Spaces 42 §2.1 Inner Product Spaces and Their Properties 42 §2.2 Hilbert Spaces 46 §2.3 The Projection Theorem 48 §2.4 Orthonormal Sets 54 §2.5 Projection in R" 58 §2.6 Linear Regression and the General Linear Model 60 §2.7 Mean Square Convergence, Conditional Expectation and Best Linear Prediction in L2(Q, , P) 62 §2.8 Fourier Series 65 §2.9 Hilbert Space Isomorphisms 67 §2.10* The Completeness of L2(Q, .F, P) 68 §2.11* Complementary Results for Fourier Series 69 Problems 73 xiv Contents CHAPTER 3 Stationary ARMA Processes 77 §3.1 Causal and Invertible ARMA Processes 77 §3.2 Moving Average Processes of Infinite Order 89 §3.3 Computing the Autocovariance Function of an ARMA(p, q) Process 91 §3.4 The Partial Autocorrelation Function 98 §3.5 The Autocovariance Generating Function 103 §3.6* Homogeneous Linear Difference Equations with Constant Coefficients 105 Problems 110 CHAPTER 4 The Spectral Representation of a Stationary Process 114 §4.1 Complex Valued Stationary Time Series 114 §4.2 The Spectral Distribution of a Linear Combination of Sinusoids 116 §4.3 Herglotz's Theorem 117 §4.4 Spectral Densities and ARMA Processes 122 §4.5* Circulants and Their Eigenvalues 133 §4.6* Orthogonal Increment Processes on [—7t,7t] 138 §4.7* Integration with Respect to an Orthogonal Increment Process 140 §4.8* The Spectral Representation 143 §4.9* Inversion Formulae 150 §4.10* Time Invariant Linear Filters 152 §4.11* Properties of the Fourier Approximation hn to I(Vj0,] 157 Problems 159 CHAPTER 5 Prediction of Stationary Processes 166 §5.1 The Prediction Equations in the Time Domain 166 §5.2 Recursive Methods for Computing Best Linear Predictors 169 §5.3 Recursive Prediction of an ARM A(p,q) Process 175 §5.4 Prediction of a Stationary Gaussian Process; Prediction Bounds 182 §5.5 Prediction of a Causal Invertible ARMA Process in Terms of Xp oo ; n 182 §5.6* Prediction in the Frequency Domain 185 §5.7* The Wold Decomposition 187 §5.8* Kolmogorov's Formula 191 Problems 192 CHAPTER 6* Asymptotic Theory 198 §6.1 Convergence in Probability 198 §6.2 Convergence in rth Mean, r 0 202 §6.3 Convergence in Distribution 204 §6.4 Central Limit Theorems and Related Results 209 Problems 215 Contents xv CHAPTER 7 Estimation of the Mean and the Autocovariance Function 218 §7.1 Estimation of /i 218 §7.2 Estimation of y(•) and p(¦) 220 §7.3* Derivation of the Asymptotic Distributions 225 Problems 236 CHAPTER 8 Estimation for ARMA Models 238 §8.1 The Yule Walker Equations and Parameter Estimation for Autoregressive Processes 239 §8.2 Preliminary Estimation for Autoregressive Processes Using the Durbin Levinson Algorithm 241 §8.3 Preliminary Estimation for Moving Average Processes Using the Innovations Algorithm 245 §8.4 Preliminary Estimation for ARMA(p,q) Processes 250 §8.5 Remarks on Asymptotic Efficiency 253 §8.6 Recursive Calculation of the Likelihood of an Arbitrary Zero Mean Gaussian Process 254 §8.7 Maximum Likelihood and Least Squares Estimation for ARMA Processes 256 §8.8 Asymptotic Properties of the Maximum Likelihood Estimators 258 §8.9 Confidence Intervals for the Parameters of a Causal Invertible ARMA Process 260 §8.10* Asymptotic Behavior of the Yule Walker Estimates 262 §8.11* Asymptotic Normality of Parameter Estimators 265 Problems 269 CHAPTER 9 Model Building and Forecasting with ARIMA Processes 273 §9.1 ARIMA Models for Non Stationary Time Series 274 §9.2 Identification Techniques 284 §9.3 Order Selection 301 §9.4 Diagnostic Checking 306 §9.5 Forecasting ARIMA Models 314 §9.6 Seasonal ARIMA Models 320 Problems 326 CHAPTER 10 Inference for the Spectrum of a Stationary Process 330 §10.1 The Periodogram 331 §10.2 Testing for the Presence of Hidden Periodicities 334 §10.3 Asymptotic Properties of the Periodogram 342 §10.4 Smoothing the Periodogram 350 §10.5 Confidence Intervals for the Spectrum 362 §10.6 Autoregressive, Maximum Entropy, Moving Average and Maximum Likelihood ARMA Spectral Estimators 365 §10.7 The Fast Fourier Transform (FFT) Algorithm 373 xvi Contents §10.8* Derivation of the Asymptotic Behavior of the Maximum Likelihood and Least Squares Estimators of the Coefficients of an ARMA Process 375 Problems 396 CHAPTER 11 Multivariate Time Series 401 §11.1 Second Order Properties of Multivariate Time Series 402 §11.2 Estimation of the Mean and Co variance Function 405 §11.3 Multivariate ARMA Processes 417 §11.4 Best Linear Predictors of Second Order Random Vectors 421 §11.5 Estimation for Multivariate ARMA Processes 430 §11.6 The Cross Spectrum 434 §11.7 Estimating the Cross Spectrum 443 §11.8* The Spectral Representation of a Multivariate Stationary Time Series 454 Problems 459 CHAPTER 12 State Space Models and the Kalman Recursions 463 §12.1 State Space Models 463 §12.2 The Kalman Recursions 474 §12.3 State Space Models with Missing Observations 482 §12.4 Controllability and Observability 489 §12.5 Recursive Bayesian State Estimation 498 Problems 501 CHAPTER 13 Further Topics 506 §13.1 Transfer Function Modelling 506 §13.2 Long Memory Processes 520 §13.3 Linear Processes with Infinite Variance 535 §13.4 Threshold Models 545 Problems 552 Appendix: Data Sets 555 Bibliography 561 Index 567
adam_txt	Contents Preface to the Second Edition vii Preface to the First Edition ix CHAPTER 1 Stationary Time Series 1 §1.1 Examples of Time Series 1 §1.2 Stochastic Processes 8 §1.3 Stationarity and Strict Stationarity 11 §1.4 The Estimation and Elimination of Trend and Seasonal Components 14 §1.5 The Autocovariance Function of a Stationary Process 25 §1.6 The Multivariate Normal Distribution 32 §1.7* Applications of Kolmogorov's Theorem 37 Problems 39 CHAPTER 2 Hilbert Spaces 42 §2.1 Inner Product Spaces and Their Properties 42 §2.2 Hilbert Spaces 46 §2.3 The Projection Theorem 48 §2.4 Orthonormal Sets 54 §2.5 Projection in R" 58 §2.6 Linear Regression and the General Linear Model 60 §2.7 Mean Square Convergence, Conditional Expectation and Best Linear Prediction in L2(Q, , P) 62 §2.8 Fourier Series 65 §2.9 Hilbert Space Isomorphisms 67 §2.10* The Completeness of L2(Q, .F, P) 68 §2.11* Complementary Results for Fourier Series 69 Problems 73 xiv Contents CHAPTER 3 Stationary ARMA Processes 77 §3.1 Causal and Invertible ARMA Processes 77 §3.2 Moving Average Processes of Infinite Order 89 §3.3 Computing the Autocovariance Function of an ARMA(p, q) Process 91 §3.4 The Partial Autocorrelation Function 98 §3.5 The Autocovariance Generating Function 103 §3.6* Homogeneous Linear Difference Equations with Constant Coefficients 105 Problems 110 CHAPTER 4 The Spectral Representation of a Stationary Process 114 §4.1 Complex Valued Stationary Time Series 114 §4.2 The Spectral Distribution of a Linear Combination of Sinusoids 116 §4.3 Herglotz's Theorem 117 §4.4 Spectral Densities and ARMA Processes 122 §4.5* Circulants and Their Eigenvalues 133 §4.6* Orthogonal Increment Processes on [—7t,7t] 138 §4.7* Integration with Respect to an Orthogonal Increment Process 140 §4.8* The Spectral Representation 143 §4.9* Inversion Formulae 150 §4.10* Time Invariant Linear Filters 152 §4.11* Properties of the Fourier Approximation hn to I(Vj0,] 157 Problems 159 CHAPTER 5 Prediction of Stationary Processes 166 §5.1 The Prediction Equations in the Time Domain 166 §5.2 Recursive Methods for Computing Best Linear Predictors 169 §5.3 Recursive Prediction of an ARM A(p,q) Process 175 §5.4 Prediction of a Stationary Gaussian Process; Prediction Bounds 182 §5.5 Prediction of a Causal Invertible ARMA Process in Terms of Xp oo ; n 182 §5.6* Prediction in the Frequency Domain 185 §5.7* The Wold Decomposition 187 §5.8* Kolmogorov's Formula 191 Problems 192 CHAPTER 6* Asymptotic Theory 198 §6.1 Convergence in Probability 198 §6.2 Convergence in rth Mean, r 0 202 §6.3 Convergence in Distribution 204 §6.4 Central Limit Theorems and Related Results 209 Problems 215 Contents xv CHAPTER 7 Estimation of the Mean and the Autocovariance Function 218 §7.1 Estimation of /i 218 §7.2 Estimation of y(•) and p(¦) 220 §7.3* Derivation of the Asymptotic Distributions 225 Problems 236 CHAPTER 8 Estimation for ARMA Models 238 §8.1 The Yule Walker Equations and Parameter Estimation for Autoregressive Processes 239 §8.2 Preliminary Estimation for Autoregressive Processes Using the Durbin Levinson Algorithm 241 §8.3 Preliminary Estimation for Moving Average Processes Using the Innovations Algorithm 245 §8.4 Preliminary Estimation for ARMA(p,q) Processes 250 §8.5 Remarks on Asymptotic Efficiency 253 §8.6 Recursive Calculation of the Likelihood of an Arbitrary Zero Mean Gaussian Process 254 §8.7 Maximum Likelihood and Least Squares Estimation for ARMA Processes 256 §8.8 Asymptotic Properties of the Maximum Likelihood Estimators 258 §8.9 Confidence Intervals for the Parameters of a Causal Invertible ARMA Process 260 §8.10* Asymptotic Behavior of the Yule Walker Estimates 262 §8.11* Asymptotic Normality of Parameter Estimators 265 Problems 269 CHAPTER 9 Model Building and Forecasting with ARIMA Processes 273 §9.1 ARIMA Models for Non Stationary Time Series 274 §9.2 Identification Techniques 284 §9.3 Order Selection 301 §9.4 Diagnostic Checking 306 §9.5 Forecasting ARIMA Models 314 §9.6 Seasonal ARIMA Models 320 Problems 326 CHAPTER 10 Inference for the Spectrum of a Stationary Process 330 §10.1 The Periodogram 331 §10.2 Testing for the Presence of Hidden Periodicities 334 §10.3 Asymptotic Properties of the Periodogram 342 §10.4 Smoothing the Periodogram 350 §10.5 Confidence Intervals for the Spectrum 362 §10.6 Autoregressive, Maximum Entropy, Moving Average and Maximum Likelihood ARMA Spectral Estimators 365 §10.7 The Fast Fourier Transform (FFT) Algorithm 373 xvi Contents §10.8* Derivation of the Asymptotic Behavior of the Maximum Likelihood and Least Squares Estimators of the Coefficients of an ARMA Process 375 Problems 396 CHAPTER 11 Multivariate Time Series 401 §11.1 Second Order Properties of Multivariate Time Series 402 §11.2 Estimation of the Mean and Co variance Function 405 §11.3 Multivariate ARMA Processes 417 §11.4 Best Linear Predictors of Second Order Random Vectors 421 §11.5 Estimation for Multivariate ARMA Processes 430 §11.6 The Cross Spectrum 434 §11.7 Estimating the Cross Spectrum 443 §11.8* The Spectral Representation of a Multivariate Stationary Time Series 454 Problems 459 CHAPTER 12 State Space Models and the Kalman Recursions 463 §12.1 State Space Models 463 §12.2 The Kalman Recursions 474 §12.3 State Space Models with Missing Observations 482 §12.4 Controllability and Observability 489 §12.5 Recursive Bayesian State Estimation 498 Problems 501 CHAPTER 13 Further Topics 506 §13.1 Transfer Function Modelling 506 §13.2 Long Memory Processes 520 §13.3 Linear Processes with Infinite Variance 535 §13.4 Threshold Models 545 Problems 552 Appendix: Data Sets 555 Bibliography 561 Index 567
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spelling	Brockwell, Peter J. 1937-2023 (DE-588)171133188 aut Time series theory and methods Peter J. Brockwell ; Richard A. Davis Second edition New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona Springer-Verlag [1991] © 1991 xvi, 577 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Hier auch später erschienene, unveränderte Nachdrucke Série chronologique Série chronologique ram Tijdreeksen gtt Time-series analysis Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Zeitreihenanalyse (DE-588)4067486-1 s DE-604 Davis, Richard A. 1952- (DE-588)173920608 aut Erscheint auch als Online-Ausgabe 978-1-4419-0320-4 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015113481&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Brockwell, Peter J. 1937-2023 Davis, Richard A. 1952- Time series theory and methods Série chronologique Série chronologique ram Tijdreeksen gtt Time-series analysis Zeitreihenanalyse (DE-588)4067486-1 gnd
subject_GND	(DE-588)4067486-1 (DE-588)4123623-3
title	Time series theory and methods
title_auth	Time series theory and methods
title_exact_search	Time series theory and methods
title_exact_search_txtP	Time series theory and methods
title_full	Time series theory and methods Peter J. Brockwell ; Richard A. Davis
title_fullStr	Time series theory and methods Peter J. Brockwell ; Richard A. Davis
title_full_unstemmed	Time series theory and methods Peter J. Brockwell ; Richard A. Davis
title_short	Time series
title_sort	time series theory and methods
title_sub	theory and methods
topic	Série chronologique Série chronologique ram Tijdreeksen gtt Time-series analysis Zeitreihenanalyse (DE-588)4067486-1 gnd
topic_facet	Série chronologique Tijdreeksen Time-series analysis Zeitreihenanalyse Lehrbuch
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015113481&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT brockwellpeterj timeseriestheoryandmethods AT davisricharda timeseriestheoryandmethods

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