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| Авторизация |
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| Percival D.B., Walden A.T. — Wavelet methods for time series analysis |
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| Предметный указатель |
 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, 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  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 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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