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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
Multiresolution analysis (MRA), via partial DWT      104 129
Multitaper SDF estimator      269 273 329—330 394 439
Multitaper SDF estimator, applied to solar physics series      278
Multitaper SDF estimator, bandwidth of      274 277—278
Multitaper SDF estimator, lack of leakage      330 446
Multitaper SDF estimator, logarithm of      276 444
Multivariate RV      393
Multivariate RV, Gaussian (normal)      400 407 441
Munk, W.H.      340 559
Musha, T.      340 559
Nanoseconds      318
Nanoteslas (nT)      219
Narrow-band frequency characteristic      396
Nason, G.P.      159 402 421—423 559
Natural ordering for wavelet packet coefficients      209—210
Negative frequency      22
Nested subspaces      460 494
Nested subspaces, approximation and detail spaces      472—473
Nested subspaces, convention for approximation spaces      461
Neugebauer, M.      556 564
Nguyen, T.      465 471 562
Nile River minima      255 295 326 341 365 386
Nile River minima, change point      387—388
Nile River minima, MLE for      386
Nile River minima, MLE for, using Haar, D(4) and LA(8) filters      392
Nile River minima, MRA for Haar MODWT      190 192
Nile River minima, physical scales      192
Nile River minima, test for homogeneity of variance      386—387
Nile River minima, wavelet variance estimates for      327
Nilometer      193
NMR      see "Nuclear magnetic resonance"
Noise DWT coefficients, correlated      440
Noise DWT coefficients, IID Gaussian (normal)      418
Noise DWT coefficients, non-IID      432 434
Noise DWT coefficients, PDFs with level      455
Noise DWT coefficients, stochastic      424 426
Noise DWT coefficients, uncorrelated      432 434
Noise transform coefficients      394 406—408 412 452
Noise transform coefficients, IID Gaussian      453
Noise transform coefficients, non-IID      403
Noise vector, IID      452
Noise vector, non-IID      452
Noise, correlated      393
Noise, Gaussian (normal)      440
Noise, IID      393 398 451—452
Noise, IID Gaussian (normal)      417
Noise, non-Gaussian      432
Noise, non-IID      393 402
Noise, uncorrelated      393
Non-decimated DWT      159
Non-Gaussian noise      432
Non-Gaussian signal DWT coefficients      450
Non-IID noise DWT coefficients      432 434
Non-IID noise transform coefficients      403
Nonboundary DWT coefficients      370
Nonboundary DWT coefficients, MLE      371—372 383—384 390
Nonboundary DWT coefficients, reduced log likelihood      371 383
Nonlinear conditional mean      417
Nonlinear estimator of signal      408
Nonlinear transform and shrinkage      408 411—412 454
Nonnegative garrote      456
Nonorthogonality of MODWT      159
Nonstationary process      1/f-type 287
Nonstationary process with nonstationary first order backward difference      294
Nonstationary process with Pth order trend plus stationary process      289 294
Nonstationary process with stationary dth order backward difference      287 368
Nonstationary process with stationary dth order backward difference, SDF      287
Nonstationary process with stationary dth order backward difference, simulation      292
Nonstationary process with stationary first order backward difference, random walk      288
Nonstationary process with stationary first order backward difference, trend plus stationary process      288
Nonstationary process with stationary second order backward difference, random run      294
Nonstationary process, continuous parameter      340
Nonstationary process, example simulation via DWT      360
Nonstationary process, long memory      284 286
Nonstationary process, long memory, DWT-based MLEs for      368
Nonstationary process, long memory, FD      284 288
Nonstationary process, long memory, PPL      281
Nonstationary process, simulation      289
Nonstationary process, simulation, via DWT      360
Normal PDF      see "Gaussian PDF"
Normal RVs      see "Gaussian RVs"
Normalization and periodized filters      34
Normalization of scaling function      468
Normalized partial energy sequence (NPES)      129 395
Normalized partial energy sequence (NPES) for electrocardiogram      128—129
Normalized partial energy sequence (NPES) for signals      395—396
Normalized partial energy sequence (NPES) for vertical ocean shear      397
Normalized partial energy sequence (NPES), using DWT coefficients      128—129 395—396 455
Normalized partial energy sequence (NPES), using ODFT coefficients      128—129 395—396
Nowak, R.D.      554
NPES      see "Normalized partial energy sequence"
Nuclear magnetic resonance (NMR)      420 424 427
Nuclear magnetic resonance (NMR), Bayesian shrinkage estimates of signal      428
Nuclear magnetic resonance (NMR), denoising, using LA(8) partial DWT      431
Nuclear magnetic resonance (NMR), denoising, using ODFT      431
Nuclear magnetic resonance (NMR), MODWT-based thresholding estimates of signal      430
Nuclear magnetic resonance (NMR), shrinkage estimates of signal      425—426
Nuclear magnetic resonance (NMR), thresholding estimates of signal      418—419 421 423
Nyquist frequency      22 87 267 315
O'Brien, J.J.      559
Octave band average, FD process      343 353
Octave band SDF estimation      316 329—330 337 343 389
Octave band-pass filter      102
Octave frequency band      297
Odd indexed subsequence and DFT      39
Odegard, J.E.      558
ODFT      see "Orthonormal discrete Fourier transform"
Ogden, R.T.      135 255 560
Oppenheim, A.V.      28 106 117 366 484 560 563
Oppenheim, G.      552 554 559
Optimal discrete WP table transform      223 251
Optimal discrete WP table transform, example of      224
Oracle      420
Ordinary least squares estimation for FD process      378
Orthogonal complement      472 496
Orthogonality principle of linear mean, square estimation      407
Orthonormal basis, approximation space with scale $\lambda_{J}$      460 495
Orthonormal basis, approximation space with scale one half      461
Orthonormal basis, approximation space with scale two      461
Orthonormal basis, approximation space with scale unity      459
Orthonormal basis, detail space with scale one half      474—475 496 500
Orthonormal basis, detail space with scale one quarter      475
Orthonormal basis, detail space with scale unity      475
Orthonormal data tapers      273
Orthonormal discrete Fourier transform (ODFT)      41 46 49 53 395 431
Orthonormal discrete Fourier transform (ODFT) and DFT      52 54
Orthonormal discrete Fourier transform (ODFT), energy preservation      47
Orthonormal discrete Fourier transform (ODFT), inverse      49
Orthonormal discrete Fourier transform (ODFT), matrix      47
Orthonormal discrete Fourier transform (ODFT), projection theorem      52
Orthonormal matrix      42—43 53
Orthonormal transform      41 394 452
Orthonormal transform of IID Gaussian RVs      263 400
Orthonormal transform of noise coefficients      394 398 406
Orthonormal transform of signal coefficients      394 398
Orthonormal transform, DWT      57 67 72
Orthonormal transform, energy preservation      43 53
Orthonormal transform, projection theorem      44 53
Orthonormality and DWT      76—77 79 95
Orthonormality property of wavelet filty      69
Outcome of RV      256
PACS (partial autocorrelation sequence)      367
Padding (extending a sample) for the DWT      141 422—423
Padding (extending a sample) with sample mean      338
Padding (extending a sample) with zeros      308 338 382 387
Padding (extending a sample) with zeros, for the FFT      440
Papoulis, A.      256 560
Paradigm for wavelet thresholding      444 449 455
Parameter and properties of DFBM process      286
Parameter and properties of FD process      285—286
Parameter and properties of FGN process      285—286
Parameter and properties of PPL process      285—286
Parameter estimation for FD process via DWT coefficients      341
Parent node for DWPT      210
Parks, T.W.      159 174 558
Parseval's theorem      23 312 314
Parseval's theorem, one finite sequence      29 36 72 170 233
Parseval's theorem, one function      38
Parseval's theorem, one infinite sequence      23 35
Parseval's theorem, two finite sequences      29 36 233
Parseval's theorem, two functions      38 467
Parseval's theorem, two infinite sequences      23 35
Partial autocorrelation sequence (PACS)      367
Partial discrete wavelet transform (DWT)      19 56 80 104 211 341 350 385 418 433 445 447 451 454
Partial discrete wavelet transform (DWT) of ECG data      126
Partial discrete wavelet transform (DWT) of FD process      342
Partial discrete wavelet transform (DWT), advanced LA(8) coefficients for electrocardiogram      127—128
Partial discrete wavelet transform (DWT), atomic clock data      13
Partial discrete wavelet transform (DWT), C(6)      126
Partial discrete wavelet transform (DWT), choice of level      145
Partial discrete wavelet transform (DWT), circularly shifted series      160—161
Partial discrete wavelet transform (DWT), D(4)      126 418 420
Partial discrete wavelet transform (DWT), decomposition of sample variance      104
Partial discrete wavelet transform (DWT), disjoint dyadic decomposition of WP table      212
Partial discrete wavelet transform (DWT), energy decomposition      15 16 95 104 151
Partial discrete wavelet transform (DWT), Haar      13—14 55 126
Partial discrete wavelet transform (DWT), inverse      419 422 425 433—434 445 454
Partial discrete wavelet transform (DWT), LA(8)      126 418—421 423—425 428 431
Partial discrete wavelet transform (DWT), LA(8), basis vectors      162
Partial discrete wavelet transform (DWT), level of      56
Partial discrete wavelet transform (DWT), matrix      79
Partial discrete wavelet transform (DWT), multiple of power of two length      104 141 150
Partial discrete wavelet transform (DWT), vectors for waveform dictionary      240
Partial DWT      see "Partial discrete wavelet transform"
Partial energy sequence      106
Partial energy sequence for maximum/minimum delay filter      488 493
Parzen, E.      272 554
PDF      see "Probability density function"
Penalty term      398
Percentage points for homogeneity of variance test      381
Percentage points for trend test      373
Percentage points of chi-square PDF      264
Percentage points of standard Gaussian (normal) PDF      257
Percival, D.B.      159 185 244 291—292 297 307 309—310 321 326 353—354 360 554 556 558—561 563
periodic extension      30
Periodicity of DFT for finite sequence      28 36
Periodicity of DFT for infinite sequence      22 35
Periodized filter      20 32—33 35 37 39—40
Periodized filter, DFT of      33—34 37 39
Periodized filter, DWT scaling filter      77 79—80 88
Periodized filter, DWT scaling filter, circularly shifted      77 79
Periodized filter, DWT scaling filter, DFT of      92 100
Periodized filter, DWT wavelet filter      71 74 80 88 92 96—97 153
Periodized filter, DWT wavelet filter, autocorrelation      72
Periodized filter, DWT wavelet filter, circularly shifted      71 77 92 153
Periodized filter, DWT wavelet filter, DFT of      92 100
Periodized filter, example      34
Periodized filter, MODWT scaling and wavelet filter      168—170 201
Periodized filter, normalization      34
Periodogram      269 298 312 314 330 394
Periodogram, asymptotic properties (independence and unbiasedness)      270
Periodogram, bias of      298
Periodogram, covariances of      270—271
Periodogram, inconsistency of      270 298
Periodogram, leakage in      272—273 329 437 439
Periodogram, logarithm of      270 432
Periodogram, mean of      270
Periodogram, smoothing of      271
Periodogram, variance of      270
Persistence of DWT coefficients      450—451 455
Pesquet, J.-C.      159 560
Peterson, S.      204 560
Phase function      25
Phase function, D(4) wavelet filter      158
Phase function, Daubechies scaling filter      106
Phase function, Haar wavelet filter      158
Phase function, LA(L) and C(L) wavelet packet filter for node (j,n)      229
Phase function, LA(L) scaling and wavelet filters      112
Phase function, wavelet packet filter for node (3,n)      253
Phillips, J.L.      556
Physical bandwidth for MODWPT of solar magnetic field      236
Physical frequency      221
Physical scale      15 59 128 134 185 243 297 315 328 334
Physical scale for MODWT details and smooth of jth level      188 192 194
Physical time width for MODWPT of solar magnetic field      236
Picard, D.      556
Piecewise power law process      321 323 328
Pilot spectrum estimator      297
Pilot spectrum estimator and unbiased Haar-based estimator      317
Point estimate      265
Polar representation of complex variable      21
Polynomial (trigonometric)      485
Popper, W.      193 560
Porter-Hudak, S.      379 555
Positive frequency      22
Posterior, expected loss      265
Posterior, mean      266 414 454
Posterior, median      266 415—416 454
Power law process      288 294 297 332 337 340
Power of two and DWT      57 67 141 150
Power of two, multiple of, and partial DWT      104 141 150
Power of two, needed with periodogram      437
Power spectrum for stationary process      267
Power spectrum, discrete Fourier empirical      48—49 55
Power spectrum, discrete wavelet empirical      160 181
Power spectrum, discrete wavelet empirical, DWT-based      62—63 66—67 156 297
Power spectrum, discrete wavelet empirical, MODWT-based      160 181
PPL process      see "Pure power law process"
Press, W.H.      56 560
Priestley, M.B.      255—256 268—269 313 560—561
Prior information      264
Prior PDF      264—265
probability      256
Probability density function (pdf)      256
Probability density function (PDF), chi-square      263
Probability density function (pdf), conditional      260 409
Probability density function (PDF), exponential      265
Probability density function (PDF), Gaussian (normal)      3 256
Probability density function (PDF), generalized Cauchy (t)      258
Probability density function (PDF), generalized Gaussian      257
Probability density function (PDF), joint      258 265 409
Probability density function (PDF), jointly Gaussian (normal)      259
Probability density function (PDF), Laplace (two-sided exponential)      257 264
Probability density function (pdf), marginal      258 265
Probability density function (PDF), prior      264—265
Probability density function (PDF), sum of two independent RVs      262 409 416
Probability density function (PDF), sum of two RVs      262
Probability density function (PDF), t      257
Probability density function (PDF), transformed RVs      258 261
Probability of false alarm      435
Projection onto subspace      45
Projection theorem      41
Projection theorem, ODFT      52
Projection theorem, orthonormal transform      44 53
Projection theorem, unitary transform      46
Pseudo-code for DWT, analysis      101 157
Pseudo-code for DWT, details and smooth      102
Pseudo-code for DWT, pyramid algorithm      100
Pseudo-code for DWT, synthesis      101 157
Pseudo-code for MODWT, analysis      177 204
Pseudo-code for MODWT, details and smooth      179
Pseudo-code for MODWT, pyramid algorithm      177 204
Pseudo-code for MODWT, synthesis      178 204
Puccio, L.      555
Pure power law process, continuous parameter      285
Pure power law process, discrete parameter      281
Pure power law process, long memory property      281
Pure power law process, parameter and properties      285—286
Pure power law process, simulation      283
Pure power law process, spectral density function (SDF)      281—282
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