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| Percival D.B., Walden A.T. — Wavelet methods for time series analysis |
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| Предметный указатель |
LA(L) wavelet function, Hoelder regularity 494
LA(L) wavelet packet filter for node (j,n), advance required 230 233
LA(L) wavelet packet filter for node (j,n), phase function 229
LA(L) wavelet packet filter for node (j,n), shift factor 230
Lai, M.-J. 106 558
Lang, M. 159 429 558
Lanning, E.N. 218 558
Laplace (two-sided exponential) PDF 257 264 413
Laplace (two-sided exponential) PDF, mean for 257
Laplace (two-sided exponential) PDF, variance for 257
Leakage 187—188 193 197
Leakage in periodogram 272—273 329 437 439
Leakage in wavelet variance 303 329—330
Leakage in wavelet variance, D(4) 332
Leakage in wavelet variance, Haar 331
Least asymmetric scaling filter see "LA(L) scaling filter"
Least asymmetric wavelet filter see "LA(L) wavelet filter"
Least squares estimation 44 53 341
Least squares estimation (ordinary) see "Ordinary least squares"
Least squares estimation (weighted) see "Weighted least squares"
Least squares estimation, FD process 374 390
Leave-one-out cross-validation 402
Leave-one-out cross-validation, DWT 422
Leave-one-out cross-validation, threshold 423—424
Lee, P.M. 266 558
Leeson, D.B. 553
Length of series, analyzed via MODWPT 231
Length of series, analyzed via MODWT 141 159 167 199 242
Length of series, general length 56 141 143—144
Length of series, multiple of power of two 104 141 150
Length of series, power of two 67 141 150
Lessi, O. 561
Level 65—67 77
Level of partial DWT 56
Level-dependent thresholding hard 445—449
Level-dependent thresholding mid 445—446
Level-dependent thresholding soft 445—446
Level-dependent thresholding SURE-based 406 449—450 453
Level-dependent thresholding universal 406 430 444—445 455
Level-dependent variance, correlated noise DWT coefficients 441 456
Level-independent thresholding hard 445—446
Level-independent thresholding mid 445—446
Level-independent thresholding soft 445—449
Level-independent thresholding universal 444—445 455
Li, B.L. 6 295 555
Liang, J. 159 174 558
Likelihood function for Gaussian stationary FD process 361 389
Likelihood function, using Gaussian nonboundary DWT coefficients 371
Lindberg, C. 558
Lindsay, R.W. 303 558
Linear estimator of signal 408
Linear minimum mean square 417
Linear phase filter 108 111 155 158
Linear phase filter, generalized 117
Linear span 459
Linear time-invariant filter 25
Lipschitz exponents 487
Liu, P.C. 303 558
Local stationarity 327 333
Log chi-square PDF versus Gaussian (normal) PDF 276
Log chi-square RV 270 272 376 390
Log chi-square RV, distribution 432—435 437
Log likelihood, DWT-based for Gaussian FD process 363
Log likelihood, DWT-based for Gaussian FD process, with unknown mean 365
Log multitaper SDF estimator 444
Log multitaper SDF estimator, covariance of 276—277
Log multitaper SDF estimator, mean of 275
Log multitaper SDF estimator, thresholding 440 444
Log multitaper SDF estimator, variance of 275
Log multitaper SDF estimator, WLSE for FD process 379
Log periodogram 270 432
Log periodogram, LSE for FD process 379
Log periodogram, mean of 270
Log periodogram, smoothing of 272
Log periodogram, thresholding and asymmetry 456
Log periodogram, thresholding for SDF estimation 432 435 439
Log periodogram, variance of 270
Log SDF estimator 433
Long memory process 16 191 279 299 340
Long memory process, analysis 17
Long memory process, autocovariance sequence 279
Long memory process, defining property 279
Long memory process, defining property and FD process 284
Long memory process, defining property and FGN 280
Long memory process, defining property and PPL process 281
Long memory process, defining property and scaling coefficients from FD process 351
Long memory process, instantaneous parameter estimation, LS 379 391
Long memory process, instantaneous parameter estimation, ML 374 391
Long memory process, nonstationary 284
Long memory process, nonstationary, FD 284 288
Long memory process, nonstationary, PPL 281
Long memory process, parameter estimation, LS 374
Long memory process, parameter estimation, ML 361 368
Long memory process, stationary 281
Long memory process, synthesis 17
loss 265
Loss, absolute error 266 415
Loss, posterior expected 265
Loss, squared error 265—266 414
Low-pass example 25 39
Low-pass filter 26
Low-pass filter, Daubechies scaling filter 76 78
Low-pass filter, Daubechies scaling filter, of second level 91
Low-pass filter, example of impulse response 25 39
Low-pass filter, example of use 26
Low-pass filter, tide removal 185
Low-pass filter, transfer function 26 39
LSE see "Least squares estimator"
Lugannani, R. 434 558
MA process see "Moving average process"
MacDonald, G.J.F. 340 559
MAD see "Median absolute deviation"
Magnitude of complex variable 21
Magnitude squared DFTs, low/high pass filtering and downsampling 209 211
Mak, M. 6 558
Malfait, M. 557
Mallat, S.G. 11 68 100 239—240 457 461 554—555 558—559
Mandelbrot, B.B. 191 279—280 559
Marginal PDF 258 265
Markov chain of first order 451
Markovian dependencies 451
Marple, S.L., Jr. 269 559
Martin, R.D. 553
Masry, E. 280 340 354 361 559
Matching pursuit 239 252 254
Matching pursuit, algorithm 239
Matching pursuit, ANOVA 240 252
Matching pursuit, approximation vector 252—253
Matching pursuit, approximations of subtidal sea level fluctuations 244—248
Matching pursuit, contrasted with best basis algorithm 241
Matching pursuit, dictionary of MODWT and constant vectors 247
Matching pursuit, dictionary of MODWT and ODFT vectors 247
Matching pursuit, dictionary of MODWT vectors 242 253
Matching pursuit, dictionary of partial DWT vectors 240
Matching pursuit, dictionary of WP table and ODFT vectors 241
Matching pursuit, dictionary of WP table vectors 241 254
Matching pursuit, energy decomposition 240 252
Matching pursuit, normalized residual sum of squares 247—248
Matching pursuit, residual vector 252—254
Matching pursuit, subtidal sea level fluctuations using MODWT dictionary 243—245
Matrix, circular shift 52 71
Matrix, complex orthonormal (unitary) 45 53
Matrix, DWT 57 63 99 156
Matrix, identity 42
Matrix, ODFT 47
Matrix, orthonormal 42—43 53
Matrix, unitary 46—47
Maximal overlap discrete wavelet packet transform (MODWPT) 231 251 278
Maximal overlap discrete wavelet packet transform (MODWPT), advanced LA(8) coefficients for solar magnetic field 235—236
Maximal overlap discrete wavelet packet transform (MODWPT), ANOVA 233 251
| Maximal overlap discrete wavelet packet transform (MODWPT), energy decomposition 233 251
Maximal overlap discrete wavelet packet transform (MODWPT), general length series 231
Maximal overlap discrete wavelet packet transform (MODWPT), non-advanced LA(8) coefficients for solar magnetic field 253
Maximal overlap discrete wavelet packet transform (MODWPT), physical bandwidth for solar magnetic field 236
Maximal overlap discrete wavelet packet transform (MODWPT), physical time width for solar magnetic field 236
Maximal overlap discrete wavelet packet transform (MODWPT), zero phase filter for details 234 237 252
Maximal overlap discrete wavelet transform (MODWT) 17 19 159 294 374—375 390
Maximal overlap discrete wavelet transform (MODWT) and cycle spinning 429
Maximal overlap discrete wavelet transform (MODWT), advanced LA(8) coefficients for electrocardiogram 182—183
Maximal overlap discrete wavelet transform (MODWT), advanced LA(8) coefficients for subtidal sea levels 189
Maximal overlap discrete wavelet transform (MODWT), analysis 175
Maximal overlap discrete wavelet transform (MODWT), ANOVA 160 166 171
Maximal overlap discrete wavelet transform (MODWT), ANOVA and circular shifts 160 180 200
Maximal overlap discrete wavelet transform (MODWT), ANOVA, for subtidal sea levels 185
Maximal overlap discrete wavelet transform (MODWT), atomic clock data 17—18
Maximal overlap discrete wavelet transform (MODWT), choice of level 188 193 199
Maximal overlap discrete wavelet transform (MODWT), circularly shifted series 179 181
Maximal overlap discrete wavelet transform (MODWT), discarded boundary coefficients 310
Maximal overlap discrete wavelet transform (MODWT), DWT coefficients via subsampling 174 203
Maximal overlap discrete wavelet transform (MODWT), energy decomposition 16—17 166 168—169 171 173 200
Maximal overlap discrete wavelet transform (MODWT), general length series 159 167 199 242
Maximal overlap discrete wavelet transform (MODWT), Haar 17—18
Maximal overlap discrete wavelet transform (MODWT), invalid ANOVA using details 182
Maximal overlap discrete wavelet transform (MODWT), inverse 429
Maximal overlap discrete wavelet transform (MODWT), LA(8) 182 430
Maximal overlap discrete wavelet transform (MODWT), MRA 166 168—169 172—173 182 200
Maximal overlap discrete wavelet transform (MODWT), nonorthogonality 159 200
Maximal overlap discrete wavelet transform (MODWT), pyramid algorithm 164—165 174—175 177 201
Maximal overlap discrete wavelet transform (MODWT), reflecting boundary conditions for 310
Maximal overlap discrete wavelet transform (MODWT), renormalized vectors for waveform dictionary 242—243
Maximal overlap discrete wavelet transform (MODWT), scaling filter see "Scaling filter MODWT"
Maximal overlap discrete wavelet transform (MODWT), synthesis 175
Maximal overlap discrete wavelet transform (MODWT), upper bounds for level 200
Maximal overlap discrete wavelet transform (MODWT), vectors for waveform dictionary 242 253
Maximal overlap discrete wavelet transform (MODWT), wavelet filter see "Wavelet filter MODWT"
Maximal overlap discrete wavelet transform (MODWT), zero phase filter for details and smooths 160 172 168 189
Maximal overlap WP table 232 251
Maximum delay dipole 488 490—491 493—494 500
Maximum delay filter 488
Maximum likelihood estimator (MLE) 341
Maximum likelihood estimator (MLE), arbitrary sample size 367 373
Maximum likelihood estimator (MLE), DWT-based for Gaussian ARFIMA process 366
Maximum likelihood estimator (MLE), DWT-based for Gaussian FD process 363—364 390
Maximum likelihood estimator (MLE), DWT-based for Gaussian FD process with unknown mean 365—366
Maximum likelihood estimator (MLE), exact for Gaussian FD process 363—364 367 372 390
Maximum likelihood estimator (MLE), exact for Gaussian FD process with unknown mean 366
Maximum likelihood estimator (MLE), Gaussian nonboundary DWT coefficients 371—372 383—384 390
Maximum likelihood estimator (MLE), Gaussian stationary FD process 361—362
Maximum likelihood estimator (MLE), Nile River minima 386 392
Maximum likelihood estimator (MLE), nonstationary FD process 368
Maximum likelihood estimator (MLE), scale restricted 373 385
Maximum phase dipole 488 490—491 493 500
Maximum phase filter 488
Mayer, M.E. 557
Mazumdar, R.R. 354 555
McCoy, E.J. 355 379 559 563
McCulloch, R.E. 554
McGill, K. 141 562
McGunigal, T.E. 553
McHardy, I. 340 559
McLeod, A.I. 361 559
Mean absolute error 261 266 411
Mean absolute error, minimization 411
Mean of chi-square RV 263 270
Mean of function of RVs 256 258
Mean of Gaussian (normal) RV 257
Mean of generalized Cauchy (t) RV 258
Mean of Laplace (two-sided exponential) RV 257
Mean of log multitaper SDF estimator 275
Mean of log periodogram 270
Mean of periodogram 270
Mean of RV 256
Mean of stationary stochastic process 266
Mean of wavelet coefficients 301 305 335
Mean square, equality in 38
Mean square, error 261 265 408 411
Mean square, error, minimization 407 409 417
Mean, conditional 260 266 394 408—411 414—415 454 456
Mean, posterior 266 414 454
Mean, sample see "Sample mean"
Median absolute deviation (MAD) standard deviation estimate 420
Median absolute deviation (MAD) standard deviation estimate, DWT-based 418—421 426—427 455
Median absolute deviation (MAD) standard deviation estimate, level-dependent 450
Median absolute deviation (MAD) standard deviation estimate, MÎDWT-based 429—430
Median, conditional 266 394 408 411 415 454
Median, posterior 266 415—416 454
Medley, M. 218 559
Mexican hat CWT 8 11
Mexican hat wavelet function 3 10 97
Mexican hat wavelet function, autocorrelation width 12
Meyer, Y. 554
Meyers, S.D. 12 559
Microseconds 318
Mid thresholding 399—400 430 444 453
Mid thresholding, energy levels 420
Mid thresholding, LA(8) MODWT 430
Mid thresholding, LA(8) partial DWT 419—420
Minimization of Stein's unbiased risk 405
Minimum delay (extremal phase) filter 106 117 488
Minimum delay dipole 488 490 494 500
Minimum mean square estimation 394
Minimum phase dipole 488 490 500
Minimum phase filter 488
Minimum unbiased risk 402
Mitra, S.K. 204 560
Mixing parameter 413
Mixture model see "Gaussian (normal) mixture model"
MLE see "Maximum likelihood estimator"
Mobile radio communications (MRC) process SDF 436
Mobile radio communications (MRC) process SDF, estimation via thresholding of log multitaper 446—447 449
Mobile radio communications (MRC) process SDF, estimation via thresholding of log periodogram 437—438
Modulo arithmetic 30
Modulus of complex variable 21
MODWPT see "Maximal overlap discrete wavelet packet transform"
MODWT see "Maximal overlap discrete wavelet transform"
Mofjeld, H. 185 244 326 560
Moment of inertia 261
Moments of wavelet function 483
Moments of wavelet function, vanishing see "Vanishing moments"
Montefusco, L. 555
Mood, A.M. 256 559
Moore — Penrose generalized inverse 167 204
Morettin, P.A. 218 559
Morlet (complex-valued) wavelet function 5
Morlet, J. 11 556
Moulin, P. 398 432—437 559
Moving average (MA) process 391
Moving average (MA) process, decorrelation via DWT 391
MRA see "Multiresolution analysis"
MRC see "Mobile radio communications"
Mulcahy, C. 56 559
Mullen, J.A., Jr. 553
Multiresolution analysis (MRA) 2 65 151 457
Multiresolution analysis (MRA), circular boundary conditions for electrocardiogram 133 140
Multiresolution analysis (MRA), finite energy function (signal) 478—479 481—482 496
Multiresolution analysis (MRA), function space 461 494
Multiresolution analysis (MRA), general length series 143
Multiresolution analysis (MRA), Haar MODWT Nile river minima 190 192
Multiresolution analysis (MRA), LA(8) MODWT for electrocardiogram 183—184
Multiresolution analysis (MRA), LA(8) MODWT for subtidal sea levels 185—187
Multiresolution analysis (MRA), LA(8) MODWT for vertical ocean shear 193—195
Multiresolution analysis (MRA), MODWT and circular shifts 160 180—181 200
Multiresolution analysis (MRA), partial DWT and circular shifts 160—161
Multiresolution analysis (MRA), partial DWT for electrocardiogram, using C(6) wavelet 129 132
Multiresolution analysis (MRA), partial DWT for electrocardiogram, using D(4) wavelet 129 131
Multiresolution analysis (MRA), partial DWT for electrocardiogram, using Haar wavelet 129—130
Multiresolution analysis (MRA), partial DWT for electrocardiogram, using LA(8) wavelet 129 133 142
Multiresolution analysis (MRA), reflecting boundary conditions for electrocardiogram 140 142
Multiresolution analysis (MRA), via DWT 65
Multiresolution analysis (MRA), via MODWT 166 168—169 172—173 182 200
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