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Percival D.B., Walden A.T. — Wavelet methods for time series analysis
Percival D.B., Walden A.T. — Wavelet methods for time series analysis

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Название: Wavelet methods for time series analysis

Авторы: Percival D.B., Walden A.T.

Аннотация:

The analysis of time series data is essential to many areas of science, engineering, finance and economics. This introduction to wavelet analysis "from the ground level and up," and to wavelet-based statistical analysis of time series focuses on practical discrete time techniques, with detailed descriptions of the theory and algorithms needed to understand and implement the discrete wavelet transforms. Numerous examples illustrate the techniques on actual time series. The many embedded exercises-with complete solutions provided in the Appendix — allow readers to use the book for self-guided study. Additional exercises can be used in a classroom setting. A Web site offers access to the time series and wavelets used in the book, as well as information on accessing software in S-Plus and other languages. Students and researchers wishing to use wavelet methods to analyze time series will find this book essential.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 611

Добавлена в каталог: 24.11.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\ell_{p}$ information cost functional      223 225 253
ÎLSE      see "Ordinary least squares"
Ñ(L) wavelet packet filter for node (j,n), advance required      230 233
Ñ(L) wavelet packet filter for node (j,n), phase function      229
Ñ(L) wavelet packet filter for node (j,n), shift factor      230
Ñircularly shifted periodized filter      111
Ñircularly shifted periodized filter, scaling filter      77 79
Ñircularly shifted periodized filter, wavelet filter      71 77 92 153
'Father' wavelet filter      80
'mother' wavelet filter      80
1/f-type processes      281
1/f-type processes, nonstationary      287
Abramovich, F.      415 426—427 552
Abramowitz, M.      257 552
Abry, P.      354 374 464 552
Absolute error loss      266 415
Absolute value of complex variable      21
ACVS      see "Autocovariance sequence"
Adaptive smoothing      272
Additive cost functional      223 251
Additive cost functional, $\ell_{p}$ information      223 225 253
Additive cost functional, entropy      223 225
Additive cost functional, entropy and cost table example      225
Additive cost functional, threshold      223 225 253
Admissibility condition      4
Aliasing      35 280 287 290
Alignment of time series with LA(L) partial DWT coefficients      115—116
Allan variance      159 297 314 321 339 354
Allan variance and Haar wavelet variance      322
Allan, D.W.      321 354 552
Amplitude modulated complex exponential (Morlet wavelet function)      5
Analysis of function, scaling coefficients      460 495
Analysis of signal, scaling coefficients      460 495
Analysis of time series      43 46 53
Analysis of time series, arbitrary disjoint dyadic decomposition      213
Analysis of time series, DWPT coefficients      209—210 212
Analysis of time series, DWT coefficients      57
Analysis of time series, Fourier coefficients      47
Analysis of time series, MODWPT coefficients      232
Analysis of time series, MODWT coefficients      169
Analysis of time series, partial DWT coefficients      80 89
Analysis of variance (Anova)      19 267 295—296 307 335
Analysis of variance (ANOVA) by frequency band      208 214 233 250—251
Analysis of variance (ANOVA), DWPT coefficients      208 250
Analysis of variance (ANOVA), invalid using MODWT details      182
Analysis of variance (ANOVA), LA(8) MODWT for subtidal sea levels      185
Analysis of variance (ANOVA), matching pursuit      240 252
Analysis of variance (ANOVA), MODWPT coefficients      233 251
Analysis of variance (ANOVA), MODWT coefficients      160 166 171
Analysis of variance (ANOVA), padding/extending a sample for the DWT      141
Analysis of variance (ANOVA), scale-by-scale      62 151
Analysis of variance (ANOVA), WP table decomposition      214
Anderson, T.W.      255 552
anova      see "Analysis of variance"
Antoniadis, A.      552 554 559
Approximation space, Haar scale one half      461
Approximation space, Haar scale two      461
Approximation space, Haar scale unity      460—461
Approximation space, scale $\lambda_{J}$      460 462 495
Approximation space, scale unity      459
AR process      see "Autoregressive process"
AR(1) process and wavelet coefficients      337
AR(1) process, ACS of nonboundary wavelet coefficients      352—353
AR(1) process, decorrelation via DWT      353
AR(1) process, SDFs      351—352
AR(2) process      436
AR(2) process, SDF      436
AR(2) process, SDF estimation via thresholding of log multitaper      446 448
AR(2) process, SDF estimation via thresholding of log periodogram      437—438
AR(2) process, standard deviation of derived noise DWT coefficients      442
AR(24) process      272—273 435
AR(24) process, SDF      435
AR(24) process, SDF estimation      273 275
AR(24) process, SDF estimation via thresholding of log multitaper      446—447
AR(24) process, SDF estimation via thresholding of log periodogram      437—438
ARE (asymptotic relative efficiency)      309
ARFIMA process      seå "Autoregressive fractionally integrated moving average process"
Argument of complex variable      21
Astronomical unit      219
Asymptotic properties of periodogram      270
Asymptotic relative efficiency of unbiased wavelet variance estimators      309
Atomic clock      295 318 341
Atomic clock average fractional frequency deviates      7—8 11 318 321—322 383 392
Atomic clock average fractional frequency deviates, MLEs      384
Atomic clock average fractional frequency deviates, MODWT      17 18
Atomic clock average fractional frequency deviates, partial DWT      13 14
Atomic clock average fractional frequency deviates, test for trend      384
Atomic clock average fractional frequency deviates, wavelet variance estimates for      322 384
Atomic clock average fractional frequency deviates, WLSEs      385
Atomic clock, wavelet variance estimates for      317 319 320
Autocorrelation sequence, FD process      345—346
Autocorrelation sequence, nonboundary wavelet coefficients from AR(1) process      352—353
Autocorrelation sequence, nonboundary wavelet coefficients from FD process      345—346
Autocorrelation sequence, stationary process      266
Autocorrelation width      12
Autocorrelation width, first difference of Gaussian      12
Autocorrelation width, Haar (alternative formulation)      12
Autocorrelation width, Haar scaling filter of jth level      103
Autocorrelation width, Mexican hat      12
Autocorrelation width, scaling filter (DWT) of jth level      103
Autocorrelation width, scaling filter (MODWT) of jth level      174
Autocorrelation, complex-valued dipole      489
Autocorrelation, DFT for finite sequence      30 37
Autocorrelation, DFT for infinite sequence      25 36
Autocorrelation, finite sequence (circular)      30 37
Autocorrelation, Fourier transform of      38
Autocorrelation, function      38
Autocorrelation, infinite sequence      25 36
Autocorrelation, periodized wavelet filter      72
Autocorrelation, real-valued dipole      488
Autocorrelation, wavelet filter      69
Autocovariance sequence      266
Autocovariance sequence, biased estimator      269
Autocovariance sequence, FD process      284 341
Autocovariance sequence, FD process, Davies — Harte simulations      359
Autocovariance sequence, FD process, DWT-based simulations      359
Autocovariance sequence, FGN      279
Autocovariance sequence, long memory process      279
Autocovariance sequence, relationship to SDF      267
Autocovariance sequence, square summability condition      267 307
Autocovariance sequence, symmetry      266
Autocovariance sequence, true versus simulated for FD process      357
Autocovariance sequence, white noise      268
Autoregressive (AR) process      351 see "AR(2)" "AR(24)"
Autoregressive (AR) process of order p (AR(p))      268
Autoregressive (AR) process, simulation      292
Autoregressive (AR) process, spectral density function      268
Autoregressive (AR) process, variance      294
Autoregressive fractionally integrated, DWT-based MLEs      366
Autoregressive fractionally integrated, moving average (ARFIMA) process      285 366
Average, air temperature      6 7
Average, fractional frequency deviates      321—322
Average, rainfall      6
Average, sea surface temperature      6 7
Average, signal over a scale      6
Average, vertical wind velocity      6
Averages, changes in      7 59
Backward difference filter      304
Backward difference filter, order L/2      107
Backward difference filter, squared gain function of      304 335
Backward difference, first      60
Backward difference, second      60
Backward shift operator      283 287
Balakrishnan, N.      557
Balek, J.      193 552
Baliunas, S.      6 552
Balogh, A.      220—221 236—237 552 556
Band-pass filter      5
Band-pass filter, Daubechies wavelet filter of jth level      96
Band-pass filter, Daubechies wavelet filter of second level      91
Bandwidth      445
Bandwidth for smoothing      269 272
Bandwidth of multitaper SDF estimator      274 277—278
Bandwidth, physical for MODWPT of solar magnetic field      236
Baraniuk, R.G.      554
Barnes, J.A.      321 553
Bartlett, M.S.      270 275—276 376 553
Baseline drift      125 128—129 134 185 197
Basis vectors for LA(8) partial DWT      162
Basis, approximation space for scale $\lambda_{J}$      460 495
Basis, approximation space with scale one half      461
Basis, approximation space with scale two      461
Basis, approximation space with scale unity      459 461
Basis, complex finite dimensional vector space      46
Basis, detail space with scale one half      474—475 496 500
Basis, detail space with scale one quarter      475
Basis, detail space with scale unity      475
Basis, real finite dimensional vector space      43—44 239
Basis, subspace of real finite dimensional vector space      45
Bassingthwaighte, J.B.      560
Bavesian statistics      264 394
Bayes estimator      265
Bayes risk      265—266
Bayesian decision rule      265
Bayesian methods      412 426
Bayesian shrinkage estimator, absolute error loss      415
Bayesian shrinkage estimator, squared error loss      426
Bayesian shrinkage rule      412—415 454
Bayesian shrinkage rule, DWT-based      426—428
Bayesian shrinkage rule, LA(8) partial DWT      428
Bayesian shrinkage rule, squared error loss of estimator      414
Beauchamp, K.G.      41 218 553
Benedetto, J.J.      562
Beran, J.      192—193 279—280 284—285 361 367 386 388 553
Berger, R.L.      256 554
Best basis algorithm      223 225 251
Best basis algorithm, boundary effects      227
Best basis algorithm, circularly shifted series      227
Best basis algorithm, contrasted with matching pursuit      241
Best basis algorithm, shift-adapted      228
Best basis algorithm, solar magnetic field      226—228
Best localized (BL) filter      119
Best localized (BL) filter, scaling filter      119
Best localized (BL) filter, scaling filter, plotted      119
Best localized (BL) filter, scaling filter, reversal from Doroslovacki      119
Best localized (BL) filter, wavelet filter, phase after advance      120
Best shift basis algorithm      228
Best shift basis algorithm, solar magnetic field      228
Best, D.J.      264 553
Beylkin, G.      159 553—554
Bias in the sample variance      299—300
Bias of periodogram      298
Bias-variance trade-off      272
Bias-variance trade-off, MODWT and DWT      431
Biased ACVS estimator      269
Biased MODWT-based estimator of the wavelet variance      307 337 351 378
Billingsley, P.      381 553
Binary vector for sequency ordering at node (j,n)      215—217 249 253
Binary-valued RV      410 454
Bjoerck, A.      280 554
BL filter      see "Best localized filter"
Blackman, R.B.      255 269 297 317 553
Bloomfield, P.      255 269 272 553
Bochsler, P.      564
Boes, D.C.      559
Bose, N.K.      562
Boundary coefficients, DWPT, delineated in plot after alignment      221
Boundary coefficients, DWPT, number of      221
Boundary coefficients, DWT      350 370
Boundary coefficients, DWT, delineated in plot after alignment      138
Boundary coefficients, DWT, number of      136 139 146 158
Boundary coefficients, DWT, time alignment      137—138 146—147
Boundary coefficients, MODWPT, delineated in plot after alignment      236
Boundary coefficients, MODWT, delineated in plot after alignment      182—183 198
Boundary coefficients, MODWT, number of      198
boundary conditions      see "Circular or reflecting"
Boundary details and smooths      139
Boundary details and smooths, DWT, delineated in plot      139—140 196
Boundary details and smooths, DWT, number of      139 149
Boundary details and smooths, MODWPT, delineated in plot      237—238
Boundary details and smooths, MODWT      198—199
Boundary details and smooths, MODWT, delineated in plot      183—184 186 192 194—196 199
Boundary details and smooths, MODWT, number of      199
Boundary wavelets      141
Box plots      442—443
Box, G.E.P.      255 266 553
Bracewell, R.N.      4 103 216 553
Bradshaw, G.A.      295 553
Briggs, W.L.      20 553
Brillinger.D.R.      255 269 368 553
Broad-band frequency characteristic      396
Brockwell, P.J.      363 367 553
Brodsky, J.      557
Brown, J.W.      20 553
Brown, R.L.      380 553
Bruce, A.G.      79 106—107 135 141 149—150 159 241 253 400 429 432 553—554
Bultheel, A.      557
Bump signal      395
Burrus, C.S.      558
Byers, S.D.      563
C(6) scaling and wavelet filters, filter coefficients      109
C(6) scaling and wavelet filters, jth level filters      125
C(6) scaling and wavelet filters, reversal from Daubechies      123
C(L) scaling and wavelet filters      123 158
C(L) scaling and wavelet filters, advance required      147 156
C(L) scaling and wavelet filters, approximately linear phase      124
C(L) scaling and wavelet filters, phase after advance      124
C(L) scaling and wavelet filters, plotted      123
C(L) scaling and wavelet filters, shift factor      124 198 205 229
Cahalan, R.F.      556
Calderon, A.P.      11 554
Carfantan, H.      560
Carlin, J.B.      555
Carmona, R.      12 255 295 554
Cartesian representation      21
Cascade of filters      27
Cascade of filters for wavelet coefficients of second level      90
Cascade of filters, D(4) wavelet filter      68
Cascade of filters, Daubechies wavelet filter      105 107
Cascade of filters, equivalent filter      28 39
Cascade of filters, flow diagram      27—28
Cascade of filters, width of equivalent filter      28
Casella, G.      256 554
Center of energy of a filter      118 231
Central limit theorem      434
Chambers, J.M.      264 554
Chan, G.      290 563
Change point      381—382 391
Change point, Nile River minima      387—388
Changes in averages      7
Chi, A.R.      553
Chi-square distribution      345
Chi-square distribution, scaled      313 336 338
Chi-square pdf      263
Chi-square PDF, percentage points      264
Chi-square RV      263 271
Chi-square RV and IID Gaussian (normal) RVs      293
Chi-square RV, log transformation      293
Chi-square RV, mean for      263 270
Chi-square RV, variance for      263 270
Chipman, H.A.      410 412—414 426—427 554
Chirp      157
Cholesky decomposition      361
Chui, C.K.      492 554—555
Churchill, R.V.      20 553
Circular autocorrelation      see "Autocorrelation (circular)"
Circular boundary conditions for DWT      60 140
Circular convolution      see "Convolution (circular)"
Circular covariance matrix      441
Circular cross-correlation      see "Cross-correlation (circular)"
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