Nonlinear time series: nonparametric and parametric methods
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Springer
2005
|
| Series: | Springer series in statistics
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 487 - 536 |
| Physical Description: | XIX, 551 S. graph. Darst. 24 cm |
| ISBN: | 0387261427 |
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| 100 | 1 | |a Fan, Jianqing |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nonlinear time series |b nonparametric and parametric methods |c Jianqing Fan ; Qiwei Yao |
| 264 | 1 | |a New York |b Springer |c 2005 | |
| 300 | |a XIX, 551 S. |b graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer series in statistics | |
| 500 | |a Literaturverz. S. 487 - 536 | ||
| 650 | 7 | |a Análise de séries temporais |2 larpcal | |
| 650 | 7 | |a Sistemas não lineares |2 larpcal | |
| 650 | 4 | |a Nonlinear theories | |
| 650 | 4 | |a Time-series analysis | |
| 650 | 0 | 7 | |a Parametrisches Verfahren |0 (DE-588)4205938-0 |2 gnd |9 rswk-swf |
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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
|
| adam_txt |
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 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Fan, Jianqing Yao, Qiwei |
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| classification_tum | MAT 634f |
| ctrlnum | (OCoLC)62674885 (DE-599)BVBBV021281129 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV021281129 |
| illustrated | Illustrated |
| index_date | 2024-07-02T13:47:10Z |
| indexdate | 2024-07-09T20:34:36Z |
| institution | BVB |
| isbn | 0387261427 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014602132 |
| oclc_num | 62674885 |
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| 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 |
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| publisher | Springer |
| record_format | marc |
| series2 | Springer series in statistics |
| spelling | Fan, Jianqing Verfasser aut Nonlinear time series nonparametric and parametric methods Jianqing Fan ; Qiwei Yao New York Springer 2005 XIX, 551 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Literaturverz. S. 487 - 536 Análise de séries temporais larpcal Sistemas não lineares larpcal Nonlinear theories Time-series analysis Parametrisches Verfahren (DE-588)4205938-0 gnd rswk-swf Nichtlineare Zeitreihenanalyse (DE-588)4276267-4 gnd rswk-swf Nichtparametrisches Verfahren (DE-588)4339273-8 gnd rswk-swf Nichtlineare Zeitreihenanalyse (DE-588)4276267-4 s Parametrisches Verfahren (DE-588)4205938-0 s DE-604 Nichtparametrisches Verfahren (DE-588)4339273-8 s Yao, Qiwei Verfasser aut text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2624012&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Regensburg application/pdf 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 Inhaltsverzeichnis |
| 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_exact_search_txtP | 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 |
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