Verfügbarkeit: Nonlinear time series | Technische Universität München

Nonlinear time series: nonparametric and parametric methods

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Bibliographische Detailangaben
Beteiligte Personen:	Fan, Jianqing (VerfasserIn), Yao, Qiwei (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York Springer 2005
Schriftenreihe:	Springer series in statistics
Schlagwörter:	Análise de séries temporais Sistemas não lineares Nonlinear theories Time-series analysis Parametrisches Verfahren Nichtlineare Zeitreihenanalyse Nichtparametrisches Verfahren
Links:	http://deposit.dnb.de/cgi-bin/dokserv?id=2624012&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014602132&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Beschreibung:	Literaturverz. S. 487 - 536
Umfang:	XIX, 551 S. graph. Darst. 24 cm
ISBN:	0387261427

Internformat

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Datensatz im Suchindex

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adam_text	Contents Preface vii 1 Introduction 1 LI Examples of Time Series .................... 1 1.2 Objectives of Time Series Analysis .............. 9 1.3 Linear Time Series Models ................... 10 1.3.1 White Noise Processes ................. 10 1.3.2 AR Models ....................... 10 1.3.3 MA Models ....................... 12 1.3.4 ARMA Models ..................... 12 1.3.5 AREMA Models ..................... 13 1.4 What Is a Nonlinear Time Series? .............. 14 1.5 Nonlinear Time Series Models ................. 16 1.5.1 A Simple Example ................... 16 1.5.2 ARCH Models ..................... 17 1.5.3 Threshold Models ................... 18 1.5.4 Nonparametric Autoregressive Models ........ 18 1.6 FVom Linear to Nonlinear Modeb ............... 20 1.6.1 Local Linear Modeling ................. 20 1.6.2 Global Spline Approximation ............. 23 1.6.3 Goodness-of-Fit Tests ................. 24 1.7 Further Reading ........................ 25 1.8 Software Implementations ................... 27 xiv Contents 2 Characteristics of Time Series 29 2.1 Stationarity ........................... 29 2.1.1 Definition ........................ 29 2.1.2 Stationary ARMA Processes ............. 30 2.1.3 Stationary Gaussian Processes ............ 32 2.1.4 Ergodic Nonlinear Models* .............. 33 2.1.5 Stationary ARCH Processes ............. 37 2.2 Autocorrelation ......................... 38 2.2.1 Autocovariance and Autocorrelation ......... 39 2.2.2 Estimation of ACVF and ACF ............ 41 2.2.3 Partial Autocorrelation ................ 43 2.2.4 ACF Plots, PACF Plots, and Examples ....... 45 2.3 Spectral Distributions ..................... 48 2.3.1 Periodic Processes ................... 49 2.3.2 Spectral Densities ................... 51 2.3.3 Linear Filters ...................... 55 2.4 Periodogram .......................... 60 2.4.1 Discrete Fourier Transforms .............. 60 2.4.2 Periodogram ...................... 62 2.5 Long-Memory Processes* ................... 64 2.5.1 Fractionally Integrated Noise ............. 65 2.5.2 Fractionally Integrated ARMA processes ....... 66 2.6 Mixing* ............................. 67 2.6.1 Mixing Conditions ................... 68 2.6.2 Inequalities ....................... 71 2.6.3 Limit Theorems for α -Mixing Processes ....... 74 2.6.4 A Central Limit Theorem for Nonparametric Regres¬ sion ........................... 76 2.7 Complements .......................... 78 2.7.1 Proof of Theorem 2.5(i) ................ 78 2.7.2 Proof of Proposition 2.3(i) ............... 79 2.7.3 Proof of Theorem 2.9 ................. 79 2.7.4 Proof of Theorem 2.10................. 80 2.7.5 Proof of Theorem 2.13................. 81 2.7.6 Proof of Theorem 2.14................. 81 2.7.7 Proof of Theorem 2.22................. 84 2.8 Additional Bibliographical Notes ............... 87 3 ARMA Modeling and Forecasting 89 3.1 Models and Background .................... 89 3.2 The Best Linear Prediction — Prewhitening ......... 91 3.3 Maximum Likelihood Estimation ............... 93 3.3.1 Estimators ....................... 93 3.3.2 Asymptotic Properties ................. 97 3.3.3 Confidence Intervals .................. 99 Contents xv 3.4 Order Determination...................... 99 3.4.1 Akaiké Information Criterion ............. 100 3.4.2 FPE Criterion for AR Modeling ........... 102 3.4.3 Bayesian Information Criterion ............ 103 3.4.4 Model Identification.................. 104 3.5 Diagnostic Checking...................... 110 3.5.1 Standardized Residuals ................ 110 3.5.2 Visual Diagnostic .................... 110 3.5.3 Tests for Whiteness .................. Ill 3.6 A Real Data Example — Analyzing German Egg Prices ... 113 3.7 Linear Forecasting ....................... 117 3.7.1 The Least Squares Predictors ............. 117 3.7.2 Forecasting in AR Processes .............. 118 3.7.3 Mean Squared Predictive Errors for AR Processes . 119 3.7.4 Forecasting in ARMA Processes ........... 120 Parametric Nonlinear Time Series Models 125 4.1 Threshold Models ........................ 125 4.1.1 Threshold Autoregressive Models ........... 126 4.1.2 Estimation and Model Identification ......... 131 4.1.3 Tests for Linearity ................... 134 4.1.4 Case Studies with Canadian Lynx Data ....... 136 4.2 ARCH and GARCH Models .................. 143 4.2.1 Basic Properties of ARCH Processes ......... 143 4.2.2 Basic Properties of GARCH Processes ........ 147 4.2.3 Estimation ....................... 156 4.2.4 Asymptotic Properties of Conditional MLEs* .... 161 4.2.5 Bootstrap Confidence Intervals ............ 163 4.2.6 Testing for the ARCH Effect ............. 165 4.2.7 ARCH Modeling of Financial Data .......... 168 4.2.8 A Numerical Example: Modeling S&P 500 Index Re¬ turns ........................... 171 4.2.9 Stochastic Volatility Models .............. 179 4.3 Bilinear Models ......................... 181 4.3.1 A Simple Example ................... 182 4.3.2 Markovian Representation ............... 184 4.3.3 Probabilistic Properties* ................ 185 4.3.4 Maximum Likelihood Estimation ........... 189 4.3.5 Bispectram ....................... 189 4.4 Additional Bibliographical notes ............... 191 Nonparametric Density Estimation 193 5.1 Introduction ........................... 193 5.2 Kernel Density Estimation ................... 194 5.3 Windowing and Whitening .................. 197 xvi Contents 5.4 Bandwidth Selection ...................... 199 5.5 Boundary Correction ...................... 202 5.6 Asymptotic Results* ...................... 204 5.7 Complements—Proof of Theorem 5.3............. 211 5.8 Bibliographical Notes ...................... 212 6 Smoothing in Time Series 215 6.1 Introduction ........................... 215 6.2 Smoothing in the Time Domain ................ 215 6.2.1 Trend and Seasonal Components ........... 215 6.2.2 Moving Averages .................... 217 6.2.3 Kernel Smoothing ................... 218 6.2.4 Variations of Kernel Smoothers ............ 220 6.2.5 Filtering ......................... 221 6.2.6 Local Linear Smoothing ................ 222 6.2.7 Other Smoothing Methods .............. 224 6.2.8 Seasonal Adjustments ................. 224 6.2.9 Theoretical Aspects* .................. 225 6.3 Smoothing in the State Domain ................ 228 6.3.1 Nonparametric Autoregression............ 228 6.3.2 Local Polynomial Fitting ............... 230 6.3.3 Properties of the Local Polynomial Estimator .... 234 6.3.4 Standard Errors and Estimated Bias ......... 241 6.3.5 Bandwidth Selection .................. 243 6.4 Spline Methods ......................... 246 6.4.1 Polynomial Splines ................... 247 6.4.2 Nonquadratic Penalized Splines ............ 249 6.4.3 Smoothing Splines ................... 251 6.5 Estimation of Conditional Densities ............. 253 6.5.1 Methods of Estimation ................. 253 6.5.2 Asymptotic Properties* ................ 256 6.6 Complements .......................... 257 6.6.1 Proof of Theorem 6.1 ................. 257 6.6.2 Conditions and Proof of Theorem 6.3 ........ 260 6.6.3 Proof of Lemma 6.1.................. 266 6.6.4 Proof of Theorem 6.5 ................. 268 6.6.5 Proof for Theorems 6.6 and 6.7............ 269 6.7 Bibliographical Notes ...................... 271 7 Spectral Density Estimation and Its Applications 27i» 7.1 Introduction ...........................275 7.2 Tapering, Kernel Estimation, and Prewhitening .......276 7.2.1 Tapering ........................ 277 7.2.2 Smoothing the Periodogram .............. 281 7.2.3 Prewhitening and Bias Reduction ........... 283 Contents xvii 7.3 Automatic Estimation of Spectral Density .......... 283 7.3.1 Least-Squares Estimators and Bandwidth Selection . 284 7.3.2 Local Maximum Likelihood Estimator ........ 286 7.3.3 Confidence Intervals .................. 289 7.4 Tests for White Noise ..................... 296 7.4.1 Fisher s Test ...................... 296 7.4.2 Generalized Likelihood Ratio Test .......... 298 7.4.3 2-Test and the Adaptive Neyman Test ....... 300 7.4.4 Other Smoothing-Based Tests ............. 302 7.4.5 Numerical Examples .................. 303 7.5 Complements .......................... 304 7.5.1 Conditions for Theorems 7.1—7.3.......... 304 7.5.2 Lemmas ......................... 305 7.5.3 Proof of Theorem 7.1 ................. 306 7.5.4 Proof of Theorem 7.2 ................. 307 7.5.5 Proof of Theorem 7.3 ................. 307 7.6 Bibliographical Notes ...................... 310 Nonparametric Models 313 8.1 Introduction ........................... 313 8.2 Multivariate Local Polynomial Regression .......... 314 8.2.1 Multivariate Kernel Functions ............. 314 8.2.2 Multivariate Local Linear Regression ......... 316 8.2.3 Multivariate Local Quadratic Regression ....... 317 8.3 Functional-Coefficient Autoregressive Model ......... 318 8.3.1 The Model ....................... 318 8.3.2 Relation to Stochastic Regression ........... 318 8.3.3 Ergodicity ....................... 319 8.3.4 Estimation of Coefficient Functions .......... 321 8.3.5 Selection of Bandwidth and Model-Dependent Variable322 8.3.6 Prediction ........................ 324 8.3.7 Examples ........................ 324 8.3.8 Sampling Properties* ................. 332 8.4 Adaptive Functional-Coefficient Autoregressive Models . . . 333 8.4.1 The Models ....................... 334 8.4.2 Existence and Identifiability .............. 335 8.4.3 Profile Least-Squares Estimation ........... 337 8.4.4 Bandwidth Selection .................. 340 8.4.5 Variable Selection ................... 340 8.4.6 Implementation ..................... 341 8.4.7 Examples ........................ 343 8.4.8 Extensions ....................... 349 8.5 Additive Models ........................ 349 8.5.1 The Models ....................... 349 8.5.2 The Backfitting Algorithm .............. 350 xviii Contents 8.5.3 Projections and Average Surface Estimators ..... 352 8.5.4 Estimability of Coefficient Functions ......... 354 8.5.5 Bandwidth Selection .................. 355 8.5.6 Examples ........................ 356 8.6 Other Nonparametric Models .................364 8.6.1 Two-Term Interaction Models ............. 365 8.6.2 Partially Linear Models ................ 366 8.6.3 Single-Index Models .................. 367 8.6.4 Multiple-Index Models ................. 368 8.6.5 An Analysis of Environmental Data ......... 371 8.7 Modeling Conditional Variance ................ 374 8.7.1 Methods of Estimating Conditional Variance .... 375 8.7.2 Univariate Setting ................... 376 8.7.3 Functional-Coefficient Models ............. 382 8.7.4 Additive Models .................... 382 8.7.5 Product Models ..................... 384 8.7.6 Other Nonparametric Models ............. 384 8.8 Complements .......................... 384 8.8.1 Proof of Theorem 8.1 ................. 384 8.8.2 Technical Conditions for Theorems 8.2 and 8.3 ... 386 8.8.3 Preliminaries to the Proof of Theorem 8.3...... 387 8.8.4 Proof of Theorem 8.3 ................. 390 8.8.5 Proof of Theorem 8.4 ................. 392 8.8.6 Conditions of Theorem 8.5 .............. 394 8.8.7 Proof of Theorem 8.5 ................. 395 8.9 Bibliographical Notes ...................... 399 9 Model Validation 405 9.1 Introduction ........................... 405 9.2 Generalized Likelihood Ratio Tests .............. 406 9.2.1 Introduction ...................... 406 9.2.2 Generalized Likelihood Ratio Test .......... 408 9.2.3 Null Distributions and the Bootstrap ......... 409 9.2.4 Power of the GLR Test ................ 414 9.2.5 Bias Reduction ..................... 414 9.2.6 Nonparametric versus Nonparametric Models .... 415 9.2.7 Choice of Bandwidth .................. 416 9.2.8 A Numerical Example ................. 417 9.3 Tests on Spectral Densities .................. 419 9.3.1 Relation with Nonparametric Regression ....... 421 9.3.2 Generalized Likelihood Ratio Tests .......... 421 9.3.3 Other Nonparametric Methods ............ 425 9.3.4 Tests Based on Rescaled Periodogram ........ 427 9.4 Autoregressive versus Nonparametric Models ........ 430 9.4.1 Functional-Coefficient Alternatives .......... 430 Contents xix 9.4.2 Additive Alternatives ................. 434 9.5 Threshold Models versus Varying-Coefficient Models .... 437 9.6 Bibliographical Notes...................... 439 10 Nonlinear Prediction 441 10.1 Features of Nonlinear Prediction ............... 441 10.1.1 Decomposition for Mean Square Predictive Errors . 441 10.1.2 Noise Amplification .................. 444 10.1.3 Sensitivity to Initial Values .............. 445 10.1.4 Multiple-Step Prediction versus a One-Step Plug-in Method ......................... 447 10.1.5 Nonlinear versus Linear Prediction .......... 448 10.2 Point Prediction ........................ 450 10.2.1 Local Linear Predictors ................ 450 10.2.2 An Example ...................... 451 10.3 Estimating Predictive Distributions .............. 454 10.3.1 Local Logistic Estimator ............... 455 10.3.2 Adjusted Nadaraya-Watson Estimator ........ 456 10.3.3 Bootstrap Bandwidth Selection ............ 457 10.3.4 Numerical Examples .................. 458 10.3.5 Asymptotic Properties ................. 463 10.3.6 Sensitivity to Initial Values: A Conditional Distribu¬ tion Approach ..................... 466 10.4 Interval Predictors and Predictive Sets ............ 470 10.4.1 Minimum-Length Predictive Sets ........... 471 10.4.2 Estimation of Minimum-Length Predictors ..... 474 10.4.3 Numerical Examples .................. 476 10.5 Complements .......................... 482 10.6 Additional Bibliographical Notes ............... 485 References 487 Author index 537 Subject index 545
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indexdate	2024-12-20T12:32:20Z
institution	BVB
isbn	0387261427
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-014602132
oclc_num	62674885
open_access_boolean
owner	DE-824 DE-91G DE-BY-TUM DE-706 DE-11 DE-355 DE-BY-UBR DE-739 DE-20
owner_facet	DE-824 DE-91G DE-BY-TUM DE-706 DE-11 DE-355 DE-BY-UBR DE-739 DE-20
physical	XIX, 551 S. graph. Darst. 24 cm
publishDate	2005
publishDateSearch	2005
publishDateSort	2005
publisher	Springer
record_format	marc
series2	Springer series in statistics
spellingShingle	Fan, Jianqing Yao, Qiwei Nonlinear time series nonparametric and parametric methods Análise de séries temporais larpcal Sistemas não lineares larpcal Nonlinear theories Time-series analysis Parametrisches Verfahren (DE-588)4205938-0 gnd Nichtlineare Zeitreihenanalyse (DE-588)4276267-4 gnd Nichtparametrisches Verfahren (DE-588)4339273-8 gnd
subject_GND	(DE-588)4205938-0 (DE-588)4276267-4 (DE-588)4339273-8
title	Nonlinear time series nonparametric and parametric methods
title_auth	Nonlinear time series nonparametric and parametric methods
title_exact_search	Nonlinear time series nonparametric and parametric methods
title_full	Nonlinear time series nonparametric and parametric methods Jianqing Fan ; Qiwei Yao
title_fullStr	Nonlinear time series nonparametric and parametric methods Jianqing Fan ; Qiwei Yao
title_full_unstemmed	Nonlinear time series nonparametric and parametric methods Jianqing Fan ; Qiwei Yao
title_short	Nonlinear time series
title_sort	nonlinear time series nonparametric and parametric methods
title_sub	nonparametric and parametric methods
topic	Análise de séries temporais larpcal Sistemas não lineares larpcal Nonlinear theories Time-series analysis Parametrisches Verfahren (DE-588)4205938-0 gnd Nichtlineare Zeitreihenanalyse (DE-588)4276267-4 gnd Nichtparametrisches Verfahren (DE-588)4339273-8 gnd
topic_facet	Análise de séries temporais Sistemas não lineares Nonlinear theories Time-series analysis Parametrisches Verfahren Nichtlineare Zeitreihenanalyse Nichtparametrisches Verfahren
url	http://deposit.dnb.de/cgi-bin/dokserv?id=2624012&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014602132&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT fanjianqing nonlineartimeseriesnonparametricandparametricmethods AT yaoqiwei nonlineartimeseriesnonparametricandparametricmethods

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