Wavelet methods for time series analysis:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
|
| Ausgabe: | 1. paperback ed., reprinted |
| Schriftenreihe: | Cambridge series in statistical and probabilistic mathematics
4 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 552 - 564 |
| Beschreibung: | XXV, 594 S. Ill., graph. Darst. |
| ISBN: | 9780521685085 9780521640688 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV036016035 | ||
| 003 | DE-604 | ||
| 005 | 20121030 | ||
| 007 | t| | ||
| 008 | 100208s2008 xx ad|| |||| 00||| eng d | ||
| 020 | |a 9780521685085 |9 978-0-521-68508-5 | ||
| 020 | |a 9780521640688 |9 978-0-521-64068-8 | ||
| 035 | |a (OCoLC)633499569 | ||
| 035 | |a (DE-599)BVBBV036016035 | ||
| 040 | |a DE-604 |b ger | ||
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| 049 | |a DE-703 |a DE-824 |a DE-945 | ||
| 084 | |a SK 845 |0 (DE-625)143262: |2 rvk | ||
| 100 | 1 | |a Percival, Donald B. |d 1946- |e Verfasser |0 (DE-588)141004851 |4 aut | |
| 245 | 1 | 0 | |a Wavelet methods for time series analysis |c Donald B. Percival ; Andrew T. Walden |
| 250 | |a 1. paperback ed., reprinted | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2008 | |
| 300 | |a XXV, 594 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge series in statistical and probabilistic mathematics |v 4 | |
| 500 | |a Literaturverz. S. 552 - 564 | ||
| 650 | 0 | 7 | |a Zeitreihenanalyse |0 (DE-588)4067486-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Wavelet |0 (DE-588)4215427-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Zeitreihenanalyse |0 (DE-588)4067486-1 |D s |
| 689 | 0 | 1 | |a Wavelet |0 (DE-588)4215427-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Walden, Andrew T. |d 1954- |e Verfasser |0 (DE-588)141005777 |4 aut | |
| 830 | 0 | |a Cambridge series in statistical and probabilistic mathematics |v 4 |w (DE-604)BV011442366 |9 4 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018908244&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-018908244 | |
Datensatz im Suchindex
| _version_ | 1824317402843709440 |
|---|---|
| adam_text |
Contents
Preface
.xiii
Conventions and Notation . xvii
1.
Introduction to Wavelets
. 1
1.0
Introduction
. 1
1.1
The Essence of a Wavelet
. 2
Comments and Extensions to Section
1.1 . 4
1.2
The Essence of Wavelet Analysis
.5
Comments and Extensions to Section
1.2 . 12
1.3
Beyond the CWT: the Discrete Wavelet Transform
. 12
Comments and Extensions to Section
1.3 . 19
2.
Review of Fourier Theory and Filters
. 20
2.0
Introduction
. 20
2.1
Complex Variables and Complex Exponentials
. 20
2.2
Fourier Transform of Infinite Sequences
. 21
2.3
Convolution/Filtering of Infinite Sequences
. 24
2.4
Fourier Transform of Finite Sequences
. 28
2.5
Circular Convolution/Filtering of Finite Sequences
. 29
2.6
Periodized Filters
. 32
Comments and Extensions to Section
2.6 . 35
2.7
Summary of Fourier Theory
. 35
2.8
Exercises
. 39
vn
viii Contents
3.
Orthonormal
Transforms of Time Series
. 41
3.0
Introduction
. 41
3.1
Basic Theory for
Orthonormal
Transforms
. 41
3.2
The Projection Theorem
. 44
3.3
Complex-Valued Transforms
. 45
3.4
The
Orthonormal
Discrete Fourier Transform
. 46
Comments and Extensions to Section
3.4 . 52
3.5
Summary
. 53
3.6
Exercises
. 54
4.
The Discrete Wavelet Transform
. 56
4.0
Introduction
. 56
4.1
Qualitative Description of the DWT
. 57
Key Facts and Definitions in Section
4.1 . 67
Comments and Extensions to Section
4.1 . 68
4.2
The Wavelet Filter
. 68
Key Facts and Definitions in Section
4.2 . 74
Comments and Extensions to Section
4.2 . 75
4.3
The Scaling Filter
. 75
Key Facts and Definitions in Section
4.3 . 78
Comments and Extensions to Section
4.3 . 79
4.4
First Stage of the Pyramid Algorithm
. 80
Key Facts and Definitions in Section
4.4 . 86
Comments and Extensions to Section
4.4 . 87
4.5
Second Stage of the Pyramid Algorithm
. 88
Key Facts and Definitions in Section
4.5 . 93
4.6
General Stage of the Pyramid Algorithm
.93
Key Facts and Definitions in Section
4.6 . 99
Comments and Extensions to Section
4.6 . 100
4.7
The Partial Discrete Wavelet Transform
. 104
4.8
Daubechies Wavelet and Scaling Filters: Form and Phase
. 105
Key Facts and Definitions in Section
4.8. 116
Comments and Extensions to Section
4.8 . 117
4.9
Coiflet Wavelet and Scaling Filters: Form and Phase
. 123
4.10
Example: Electrocardiogram Data
. 125
Comments and Extensions to Section
4.10. 134
4.11
Practical Considerations
. 135
Comments and Extensions to Section
4.11 . 145
4.12
Summary
. 150
4.13
Exercises
. 156
Contents ix
5. The Maximal
Overlap Discrete Wavelet Transform
. 159
5.0
Introduction
. 159
5.1
Effect of Circular Shifts on the DWT
. 160
5.2
MODWT Wavelet and Scaling Filters
. 163
5.3
Basic Concepts for MODWT
. 164
Key Facts and Definitions in Section
5.3. 168
5.4
Definition of jth Level MODWT Coefficients
. 169
Key Facts and Definitions in Section
5.4. 173
Comments and Extensions to Section
5.4 . 174
5.5
Pyramid Algorithm for the MODWT
. 174
Key Facts and Definitions in Section
5.5. 177
Comments and Extensions to Section
5.5 . 177
5.6
MODWT Analysis of 'Bump' Time Series
. 179
5.7
Example: Electrocardiogram Data
. 182
5.8
Example: Subtidal Sea Level Fluctuations
. 185
5.9
Example: Nile River Minima
. 190
5.10
Example: Ocean Shear Measurements
. 193
5.11
Practical Considerations
. 195
5.12
Summary
. 200
5.13
Exercises
. 204
6.
The Discrete Wavelet Packet Transform
. 206
6.0
Introduction
. 206
6.1
Basic Concepts
. 207
Comments and Extensions to Section
6.1 . 217
6.2
Example: DWPT of Solar Physics Data
. 218
6.3
The Best Basis Algorithm
. 221
Comments and Extensions to Section
6.3 . 226
6.4
Example: Best Basis for Solar Physics Data
. 226
6.5
Time Shifts for Wavelet Packet Filters
. 229
Comments and Extensions to Section
6.5 . 231
6.6
Maximal Overlap Discrete Wavelet Packet Transform
. 231
6.7
Example: MODWPT of Solar Physics Data
.234
6.8
Matching Pursuit
. 239
6.9
Example: Subtidal Sea Levels
. 243
Comments and Extensions to Section
6.9 . 247
6.10
Summary
. 247
6.11
Exercises
. 253
7.
Random Variables and Stochastic Processes
. 255
7.0
Introduction
. 255
7.1
Univariate Random Variables and PDFs
. 256
7.2
Random Vectors and PDFs
. 258
7.3
A Bayesian Perspective
. 264
7.4
Stationary Stochastic Processes
. 266
7.5
Spectral Density Estimation
. 269
x
Contents
Comments and Extensions to Section
7.5 . 278
7.6
Definition and Models for Long Memory Processes
. 279
Comments and Extensions to Section
7.6 . 285
7.7
Nonstationary
1//-Type
Processes
. 287
Comments and Extensions to Section
7.7 . 289
7.8
Simulation of Stationary Processes
. 290
Comments and Extensions to Section
7.8 . 292
7.9
Simulation of Stationary
Autoregressive
Processes
. 292
7.10
Exercises
. 293
8.
The Wavelet Variance
. 295
8.0
Introduction
. 295
8.1
Definition and
nationale
for the Wavelet Variance
. 295
Comments and Extensions to Section
8.1 . 301
8.2
Basic Properties of the Wavelet Variance
. 304
Comments and Extensions to Section
8.2 . 306
8.3
Estimation of the Wavelet Variance
. 306
Comments and Extensions to Section
8.3 . 308
8.4
Confidence Intervals for the Wavelet Variance
.311
Comments and Extensions to Section
8.4 . 315
8.5
Spectral Estimation via the Wavelet Variance
. 315
Comments and Extensions to Section
8.5 . 317
8.6
Example: Atomic Clock Deviates
. 317
8.7
Example: Subtidal Sea Level Fluctuations
. 324
8.8
Example: Nile River Minima
. 326
8.9
Example: Ocean Shear Measurements
. 327
8.10
Summary
. 335
8.11
Exercises
. 337
9.
Analysis and Synthesis of Long Memory Processes
. 340
9.0
Introduction
. 340
9.1
Discrete Wavelet Transform of a Long Memory Process
. 341
Comments and Extensions to Section
9.1 . 350
9.2
Simulation of a Long Memory Process
. 355
Comments and Extensions to Section
9.2 . 361
9.3
MLEs for Stationary FD Processes
. 361
Comments and Extensions to Section
9.3 . 366
9.4
MLEs for Stationary or Nonstationary FD Processes
. 368
Comments and Extensions to Section
9.4 . 373
9.5
Least Squares Estimation for FD Processes
. 374
Comments and Extensions to Section
9.5 . 378
9.6
Testing for Homogeneity of Variance
. 379
Comments and Extensions to Section
9.6 . 382
9.7
Example: Atomic Clock Deviates
. 383
9.8
Example: Nile River Minima
. 386
9.9
Summary
. 388
Contents xi
9.10
Exercises
. 391
10.
Wavelet-Based Signal Estimation
. 393
10.0
Introduction
. 393
10.1
Signal Representation via Wavelets
. 394
10.2
Signal Estimation via Thresholding
. 398
10.3
Stochastic Signal Estimation via Scaling
. 407
10.4
Stochastic Signal Estimation via Shrinkage
. 408
Comments and Extensions to Section
10.4 . 415
10.5
IID Gaussian Wavelet Coefficients
. 417
Comments and Extensions to Section
10.5 .429
10.6
Uncorrelated Non-Gaussian Wavelet Coefficients
. 432
Comments and Extensions to Section
10.6 . 439
10.7
Correlated Gaussian Wavelet Coefficients
. 440
Comments and Extensions to Section
10.7 . 449
10.8
Clustering and Persistence of Wavelet Coefficients
. 450
10.9
Summary
. 452
10.10
Exercises
.455
11.
Wavelet Analysis of Finite Energy Signals
. 457
11.0
Introduction
. 457
11.1
Translation and Dilation
. 457
11.2
Scaling Functions and Approximation Spaces
. 459
Comments and Extensions to Section
11.2 . 462
11.3
Approximation of Finite Energy Signals
. 462
Comments and Extensions to Section
11.3. 464
11.4
Two-Scale Relationships for Scaling Functions
. 464
11.5
Scaling Functions and Scaling Filters
. 469
Comments and Extensions to Section
11.5 . 472
11.6
Wavelet Functions and Detail Spaces
. 472
11.7
Wavelet Functions and Wavelet Filters
.476
11.8
Multiresolution Analysis of Finite Energy Signals
. 478
11.9
Vanishing Moments
. 483
Comments and Extensions to Section
11.9 . 486
11.10
Spectral Factorization and Filter Coefficients
. 487
Comments and Extensions to Section
11.10.494
11.11
Summary
. 494
11.12
Exercises
.500
Appendix. Answers to Embedded Exercises
. 501
References
. 552
Author Index
. 565
Subject Index
. 569 |
| any_adam_object | 1 |
| author | Percival, Donald B. 1946- Walden, Andrew T. 1954- |
| author_GND | (DE-588)141004851 (DE-588)141005777 |
| author_facet | Percival, Donald B. 1946- Walden, Andrew T. 1954- |
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| bvnumber | BV036016035 |
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| id | DE-604.BV036016035 |
| illustrated | Illustrated |
| indexdate | 2025-02-17T15:04:11Z |
| institution | BVB |
| isbn | 9780521685085 9780521640688 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018908244 |
| oclc_num | 633499569 |
| open_access_boolean | |
| owner | DE-703 DE-824 DE-945 |
| owner_facet | DE-703 DE-824 DE-945 |
| physical | XXV, 594 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge series in statistical and probabilistic mathematics |
| series2 | Cambridge series in statistical and probabilistic mathematics |
| spelling | Percival, Donald B. 1946- Verfasser (DE-588)141004851 aut Wavelet methods for time series analysis Donald B. Percival ; Andrew T. Walden 1. paperback ed., reprinted Cambridge [u.a.] Cambridge Univ. Press 2008 XXV, 594 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge series in statistical and probabilistic mathematics 4 Literaturverz. S. 552 - 564 Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Wavelet (DE-588)4215427-3 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 s Wavelet (DE-588)4215427-3 s DE-604 Walden, Andrew T. 1954- Verfasser (DE-588)141005777 aut Cambridge series in statistical and probabilistic mathematics 4 (DE-604)BV011442366 4 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018908244&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Percival, Donald B. 1946- Walden, Andrew T. 1954- Wavelet methods for time series analysis Cambridge series in statistical and probabilistic mathematics Zeitreihenanalyse (DE-588)4067486-1 gnd Wavelet (DE-588)4215427-3 gnd |
| subject_GND | (DE-588)4067486-1 (DE-588)4215427-3 |
| title | Wavelet methods for time series analysis |
| title_auth | Wavelet methods for time series analysis |
| title_exact_search | Wavelet methods for time series analysis |
| title_full | Wavelet methods for time series analysis Donald B. Percival ; Andrew T. Walden |
| title_fullStr | Wavelet methods for time series analysis Donald B. Percival ; Andrew T. Walden |
| title_full_unstemmed | Wavelet methods for time series analysis Donald B. Percival ; Andrew T. Walden |
| title_short | Wavelet methods for time series analysis |
| title_sort | wavelet methods for time series analysis |
| topic | Zeitreihenanalyse (DE-588)4067486-1 gnd Wavelet (DE-588)4215427-3 gnd |
| topic_facet | Zeitreihenanalyse Wavelet |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018908244&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011442366 |
| work_keys_str_mv | AT percivaldonaldb waveletmethodsfortimeseriesanalysis AT waldenandrewt waveletmethodsfortimeseriesanalysis |