Applied time series analysis with R:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton ; London ; New York
CRC Press, Taylor & Francis Group
[2017]
|
| Edition: | Second edition |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | A Chapmann & Hall book |
| Physical Description: | xv, 618 Seiten Illustrationen, Diagramme |
| ISBN: | 9781498734226 |
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MARC
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| 245 | 1 | 0 | |a Applied time series analysis with R |c Wayne A. Woodward (Southern Methodist University, Dallas, Texas, USA), Henry L. Gray (Southern Methodist University, Dallas, Texas, USA), Alan C. Elliott (Southern Methodist University, Dallas, Texas, USA) |
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| 264 | 1 | |a Boca Raton ; London ; New York |b CRC Press, Taylor & Francis Group |c [2017] | |
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Record in the Search Index
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|---|---|
| adam_text | APPLIED
TIME SERIES
ANALYSIS
WITH R
Second Edition
Wayne A Woodward
Southern Methodist University
Dallas, Texas, USA
Henry L Gray
Southern Methodist University
Dallas, Texas, USA
Alan C Elliott
Southern Methodist University
Dallas, Texas, USA
CRC Press is an imprint of the
Taylor Sc Francis Croup, an informa business
A CHAPMAN St HALL BOOK
CRC Press
Taylor amp; Francis Croup
Boca Raton London New York
Contents
Preface for Second Edition xiii
Acknowledgments xv
1 Stationary Time Series 1
1 1 Time Series 3
1 2 Stationary Time Series 5
1 3 Autocovariance and Autocorrelation Functions
for Stationary Time Series 7
1 4 Estimation of the Mean, Autocovariance, and
Autocorrelation for Stationary Time Series 11
141 Estimation of fi 12
1411 Ergodicity of X 12
1412 Variance of X 17
142 Estimation of yk 18
143 Estimation of pk 20
1 5 Power Spectrum 22
1 6 Estimating the Power Spectrum and Spectral Density
for Discrete Time Series 32
1 7 Time Series Examples 36
171 Simulated Data 36
172 Real Data 41
Appendix 1 A: Fourier Series 46
Appendix IB: R Commands 48
Exercises 53
2 Linear Filters 61
2 1 Introduction to Linear Filters 61
211 Relationship between the Spectra of the Input
and Output of a Linear Filter 63
2 2 Stationary General Linear Processes 63
221 Spectrum and Spectral Density for a General
Linear Process 65
2 3 Wold Decomposition Theorem 66
2 4 Filtering Applications 66
241 Butterworth Filters 69
Appendix 2A: Theorem Poofs 75
Appendix 2B: R Commands 78
Exercises 78
v
VI
Contents
3 ARM A Time Series Models 83
3 1 MA Processes 83
311 MA(1) Model 86
312 MA(2) Model 88
3 2 AR Processes 89
321 Inverting the Operator 93
322 AR(1) Model 94
323 AR(p) Model for p 1 100
324 Autocorrelations of an AR(p) Model 101
325 Linear Difference Equations 102
326 Spectral Density of an AR(p) Model 105
327 AR(2) Model 105
3271 Autocorrelations of an AR(2) Model 105
3272 Spectral Density of an AR(2) 109
3273 Stationary/Causal Region of an AR(2) 109
3274 ^-Weights of an AR(2) Model 109
328 Summary of AR(1) and AR(2) Behavior 117
329 AR(p) Model 119
3 2 10 AR(1) and AR(2) Building Blocks of an
AR(p) Model 122
3 2 11 Factor Tables 124
3 2 12 Invertibility/Infinite-Order AR Processes 131
3 2 13 Two Reasons for Imposing Invertibility 132
3 3 ARMA Processes 133
331 Stationarity and Invertibility Conditions for an
ARMA(p,^) Model 136
332 Spectral Density of an ARMA(p,q) Model 136
333 Factor Tables and ARMA(p^) Models 137
334 Autocorrelations of an ARMA(p,^) Model 140
335 ^/-Weights of an ARMA(p^) 144
336 Approximating ARMA(p^) Processes Using
High-Order AR(p) Models 146
3 4 Visualizing AR Components 146
3 5 Seasonal ARMA(p,q) x (PS/QS)S Models 149
3 6 Generating Realizations from ARMA(p^) Processes 155
361 MA(^) Model 155
362 AR(2) Model 155
363 General Procedure 156
3 7 Transformations 157
371 Memoryless Transformations 157
372 AR Transformations 158
Appendix 3A: Proofs of Theorems 161
Appendix 3B: R Commands 166
Exercises 172
Contents
vii
4 Other Stationary Time Series Models 181
4 1 Stationary Harmonic Models 181
411 Pure Harmonic Models 183
412 Harmonic Signal-Plus-Noise Models 185
413 ARMA Approximation to the Harmonic
Signal-Plus-Noise Model 187
4 2 ARCH and GARCH Processes 191
421 ARCH Processes 193
4211 The ARCH(l) Model 193
4212 The ARCH(^0) Model 196
422 The GARCH(p0/ q0) Process 197
423 AR Processes with ARCH or GARCH Noise 199
Appendix 4A: R Commands 201
Exercises 202
5 Nonstationary Time Series Models 205
5 1 Deterministic Signal-Plus-Noise Models 205
511 Trend-Component Models 206
512 Harmonic Component Models 208
5 2 ARIMA^d,^) and ARUMA^d,^) Processes 210
521 Extended Autocorrelations of an ARUMA{p,d,q)
Process 211
522 Cyclical Models 217
5 3 Multiplicative Seasonal ARUMA (p,d,q) x (Ps, Ds, Qs)s Process 217
531 Factor Tables for Seasonal Models of the Form
of Equation 5 17 with s=4 and s = 12 218
5 4 Random Walk Models 220
541 Random Walk 220
542 Random Walk with Drift 221
5 5 G-Stationary Models for Data with Time-Varying
Frequencies 221
Appendix 5A: R Commands 222
Exercises 225
6 Forecasting 229
6 1 Mean-Square Prediction Background 230
6 2 Box-Jenkins Forecasting for ARMA(p,q) Models 232
621 General Linear Process Form of the Best
Forecast Equation 233
6 3 Properties of the Best Forecast Xk) (€) 233
6 4 ^-Weight Form of the Forecast Function 235
6 5 Forecasting Based on the Difference Equation 236
651 Difference Equation Form of the Best Forecast
Equation 237
Contents
viii
652 Basic Difference Equation Form for
Calculating Forecasts from an ARMA(p^) Model 238
6 6 Eventual Forecast Function 242
6 7 Assessing Forecast Performance 243
671 Probability Limits for Forecasts 243
672 Forecasting the Last k Values 247
6 8 Forecasts Using AKUMA(p,d,q) Models 248
6 9 Forecasts Using Multiplicative Seasonal ARUMA Models 255
6 10 Forecasts Based on Signal-Plus-Noise Models 259
Appendix 6A: Proof of Projection Theorem 262
Appendix 6B: Basic Forecasting Routines 264
Exercises 268
7 Parameter Estimation 273
7 1 Introduction 273
7 2 Preliminary Estimates 274
721 Preliminary Estimates for AR(p) Models 274
7211 Yule-Walker Estimates 274
7212 Least Squares Estimation 276
7213 Burg Estimates 278
722 Preliminary Estimates for MA(q) Models 280
7221 MM Estimation for an MA(q) 280
7 22 2 MA(q) Estimation Using the
Innovations Algorithm 281
723 Preliminary Estimates for ARMA(p,^) Models 283
7231 Extended Yule-Walker Estimates of the
AR Parameters 283
7 23 2 Tsay-Tiao Estimates of the AR Parameters 284
7233 Estimating the MA Parameters 285
7 3 ML Estimation of ARMA(p^) Parameters 286
731 Conditional and Unconditional ML Estimation 286
732 ML Estimation Using the Innovations Algorithm 291
7 4 Backcasting and Estimating al 292
7 5 Asymptotic Properties of Estimators 295
751 ARCase 295
7511 Confidence Intervals: AR Case 296
752 ARMA(p^) Case 297
7521 Confidence Intervals for ARMA(p^)
Parameters 300
753 Asymptotic Comparisons of Estimators for an MA(1) 301
7 6 Estimation Examples Using Data 303
7 7 ARM A Spectral Estimation 309
7 8 ARUMA Spectral Estimation 313
Appendix 315
Exercises 317
Contents
ix
8 Model Identification 321
8 1 Preliminary Check for White Noise 321
8 2 Model Identification for Stationary ARMA Models 324
821 Model Identification Based on AIC and
Related Measures 325
8 3 Model Identification for Nonstationary
ARUMA(p,d,q) Models 328
831 Including a Nonstationary Factor in the Model 330
832 Identifying Nonstationary Component(s) in a Model 330
833 Decision Between a Stationary or a Nonstationary
Model 335
834 Deriving a Final ARUMA Model 335
835 More on the Identification of Nonstationary
Components 338
8351 Including a Factor (1 - B)d in the Model 338
8352 Testing for a Unit Root 341
8353 Including a Seasonal Factor (1 - Bs)
in the Model 344
Appendix 8A: Model Identification Based on Pattern Recognition 353
Appendix 8B: Model Identification Functions in t swge 368
Exercises 371
9 Model Building 375
9 1 Residual Analysis 375
911 Check Sample Autocorrelations of Residuals
versus 95% Limit Lines 376
912 Ljung-Box Test 376
913 Other Tests for Randomness 377
914 Testing Residuals for Normality 380
9 2 Stationarity versus Nonstationarity 380
9 3 Signal-Plus-Noise versus Purely Autocorrelation-Driven
Models 386
931 Cochrane-Orcutt and Other Methods 386
932A Bootstrapping Approach 388
933 Other Methods for Trend Testing 388
9 4 Checking Realization Characteristics 389
9 5 Comprehensive Analysis of Time Series Data: A Summary 394
Appendix 9A: R Commands 395
Exercises 396
10 Vector-Valued (Multivariate) Time Series 399
10 1 Multivariate Time Series Basics 399
10 2 Stationary Multivariate Time Series 401
10 2 1 Estimating the Mean and Covariance for Stationary
Multivariate Processes 406
X
Contents
10 211 Estimating// 406
10 212 Estimating T(k) 406
10 3 Multivariate (Vector) ARMA Processes 407
10 3 1 Forecasting Using VAR(p) Models 414
10 3 2 Spectrum of a VAR(p) Model 416
10 3 3 Estimating the Coefficients of a VAR(p) Model 416
10 331 Yule-Walker Estimation 416
10 332 Least Squares and Conditional ML
Estimation 417
10 333 Burg-Type Estimation 418
10 3 4 Calculating the Residuals and Estimating Ta 418
10 3 5 VAR(p) Spectral Density Estimation 419
10 3 6 Fitting a VAR(p) Model to Data 419
10 361 Model Selection 419
10 362 Estimating the Parameters 419
10 363 Testing the Residuals for White Noise 419
10 4 Nonstationary VARMA Processes 421
10 5 Testing for Association between Time Series 422
10 5 1 Testing for Independence of Two Stationary
Time Series 424
10 5 2 Testing for Cointegration between Nonstationary
Time Series 427
10 6 State-Space Models 429
10 6 1 State Equation 429
10 6 2 Observation Equation 429
10 6 3 Goals of State-Space Modeling 432
10 6 4 Kalman Filter 433
10 641 Prediction (Forecasting) 433
10 642 Filtering 433
10 643 Smoothing Using the Kalman Filter 434
10 644 h-Step Ahead Predictions 434
10 6 5 Kalman Filter and Missing Data 436
10 6 6 Parameter Estimation 439
10 6 7 Using State-Space Methods to Find Additive
Components of a Univariate AR Realization 440
10 671 Revised State-Space Model 441
10 672 f Real 441
10 673 Complex 442
Appendix 10A: Derivation of State-Space Results 443
Appendix 10B: Basic Kalman Filtering Routines 449
Exercises 452
11 Long-Memory Processes 455
11 1 Long Memory 456
11 2 Fractional Difference and FARM A Processes 457
Contents xi
11 3 Gegenbauer and GARMA Processes 464
11 3 1 Gegenbauer Polynomials 464
11 3 2 Gegenbauer Process 465
11 3 3 GARMA Process 469
11 4 ^-Factor Gegenbauer and GARMA Processes 472
11 4 1 Calculating Autocovariances 476
11 4 2 Generating Realizations 478
11 5 Parameter Estimation and Model Identification 479
11 6 Forecasting Based on the k-Factor GARMA Model 483
11 7 Testing for Long Memory 484
11 7 1 Testing for Long Memory in the Fractional
and FARMA Setting 486
11 7 2 Testing for Long Memory in the Gegenbauer Setting 486
11 8 Modeling Atmospheric C02 Data Using Long-Memory
Models 487
Appendix 11 A: R Commands 490
Exercises 497
12 Wavelets 499
12 1 Shortcomings of Traditional Spectral Analysis for TVF Data 499
12 2 Window-Based Methods that Localize the “Spectrum
in Time 502
12 2 1 Gabor Spectrogram 502
12 2 2 Wigner-Ville Spectrum 505
12 3 Wavelet Analysis 505
12 3 1 Fourier Series Background 506
12 3 2 Wavelet Analysis Introduction 506
12 3 3 Fundamental Wavelet Approximation Result 510
12 3 4 Discrete Wavelet Transform for Data Sets of Finite
Length 512
12 3 5 Pyramid Algorithm 515
12 3 6 Multiresolution Analysis 516
12 3 7 Wavelet Shrinkage 521
12 3 8 Scalogram: Time-Scale Plot 524
12 3 9 Wavelet Packets 527
12 3 10 Two-Dimensional Wavelets 534
12 4 Concluding Remarks on Wavelets 537
Appendix 12A: Mathematical Preliminaries for This Chapter 539
Appendix 12B: Mathematical Preliminaries 541
Exercises 545
13 G-Stationary Processes 547
13 1 Generalized-Stationary Processes 547
13 1 1 General Strategy for Analyzing G-Stationary
Processes
548
Contents
xii
13 2 M-Stationary Processes 549
13 2 1 Continuous M-Stationary Process 549
13 2 2 Discrete M-Stationary Process 551
13 2 3 Discrete Euler(p) Model 551
13 2 4 Time Transformation and Sampling 552
13 3 G(2)-Stationary Processes 556
13 3 1 Continuous G(p; A) Model 557
13 3 2 Sampling the Continuous G(A)-Stationary Processes 559
13 321 Equally Spaced Sampling from G(p; A)
Processes 560
13 3 3 Analyzing TVF Data Using the G(p; A) Model 561
13 331 G(p; A) Spectral Density 563
13 4 Linear Chirp Processes 573
13 4 1 Models for Generalized Linear Chirps 576
13 5 G-Filtering 579
13 6 Concluding Remarks 582
Appendix 13A: G-Stationary Basics 583
Appendix 13B: R Commands 587
Exercises 592
References 595
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| spelling | Woodward, Wayne A. aut Applied time series analysis with R Wayne A. Woodward (Southern Methodist University, Dallas, Texas, USA), Henry L. Gray (Southern Methodist University, Dallas, Texas, USA), Alan C. Elliott (Southern Methodist University, Dallas, Texas, USA) Second edition Boca Raton ; London ; New York CRC Press, Taylor & Francis Group [2017] © 2017 xv, 618 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier A Chapmann & Hall book Time-series analysis R (Computer program language) Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 s DE-604 Gray, Harry L. 1932- (DE-588)135805317 aut Elliott, Alan C. 1952- (DE-588)1129709353 aut DE-601 pdf/application http://zbmath.org/?q=an:1352.62007 Zentralblatt MATH Inhaltstext HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029954938&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Woodward, Wayne A. Gray, Harry L. 1932- Elliott, Alan C. 1952- Applied time series analysis with R Time-series analysis R (Computer program language) Zeitreihenanalyse (DE-588)4067486-1 gnd |
| subject_GND | (DE-588)4067486-1 |
| title | Applied time series analysis with R |
| title_auth | Applied time series analysis with R |
| title_exact_search | Applied time series analysis with R |
| title_full | Applied time series analysis with R Wayne A. Woodward (Southern Methodist University, Dallas, Texas, USA), Henry L. Gray (Southern Methodist University, Dallas, Texas, USA), Alan C. Elliott (Southern Methodist University, Dallas, Texas, USA) |
| title_fullStr | Applied time series analysis with R Wayne A. Woodward (Southern Methodist University, Dallas, Texas, USA), Henry L. Gray (Southern Methodist University, Dallas, Texas, USA), Alan C. Elliott (Southern Methodist University, Dallas, Texas, USA) |
| title_full_unstemmed | Applied time series analysis with R Wayne A. Woodward (Southern Methodist University, Dallas, Texas, USA), Henry L. Gray (Southern Methodist University, Dallas, Texas, USA), Alan C. Elliott (Southern Methodist University, Dallas, Texas, USA) |
| title_short | Applied time series analysis with R |
| title_sort | applied time series analysis with r |
| topic | Time-series analysis R (Computer program language) Zeitreihenanalyse (DE-588)4067486-1 gnd |
| topic_facet | Time-series analysis R (Computer program language) Zeitreihenanalyse |
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