initfilterdaub_dwt_discrete.m

计算时间序列的Hurst系数有许多方法

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                       %
%   initfilterDaub_DWT_discrete.m                       %
%                                                       %
%        D. Veitch   P.Abry                             %
%                                                       %
%   Melbourne  15/1/99                                  %
%   Modified DV May 99 (trun'd to 0.001 and symmetrized)%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%    This function provides the stored filters I(m) for Daubechies wavelets with N=1,2,..., 10,
%    calculated using calc_initfilterDWT_discrete.m . They are used when using the DWT 
%    to analyse intrinsically discrete time series X(k).
%
%
%  Input:   regu:  (regularity) =  number of vanishing moments (of the Daubechies wavelet).
%
%  Output:  I: The filter coefficents
%           nI: The index into the Matlab vector I corresponding to  the element m=0.
%
%  The output is the same as that of calc_initfilterDWT_discrete.m 


function [I,nI] = initfilterDaub_DWT_discrete(regu);

if ~(regu<11 & regu>0),
	mess=[' Ondelette non implantee'];
	disp(mess);
	I = []; nI=0; return;
else
% symmetric filters: being truncations to 0.00100 of original output of calc_initfilterDWT_discrete(N,0.0001) with nbvoies3 = 14
if regu==1
  I = [ -0.001006
 0.001011
 -0.001016
 0.001021
 -0.001026
 0.001031
 -0.001037
 0.001042
 -0.001047
 0.001053
 -0.001058
 0.001064
 -0.001069
 0.001075
 -0.001081
 0.001087
 -0.001092
 0.001098
 -0.001104
 0.001110
 -0.001116
 0.001123
 -0.001129
 0.001135
 -0.001142
 0.001148
 -0.001155
 0.001161
 -0.001168
 0.001175
 -0.001182
 0.001189
 -0.001196
 0.001203
 -0.001210
 0.001217
 -0.001224
 0.001232
 -0.001239
 0.001247
 -0.001255
 0.001263
 -0.001270
 0.001279
 -0.001287
 0.001295
 -0.001303
 0.001312
 -0.001320
 0.001329
 -0.001338
 0.001346
 -0.001355
 0.001365
 -0.001374
 0.001383
 -0.001393
 0.001402
 -0.001412
 0.001422
 -0.001432
 0.001442
 -0.001453
 0.001463
 -0.001474
 0.001485
 -0.001496
 0.001507
 -0.001518
 0.001529
 -0.001541
 0.001553
 -0.001565
 0.001577
 -0.001589
 0.001602
 -0.001615
 0.001628
 -0.001641
 0.001654
 -0.001668
 0.001682
 -0.001696
 0.001710
 -0.001725
 0.001739
 -0.001754
 0.001770
 -0.001785
 0.001801
 -0.001817
 0.001834
 -0.001851
 0.001868
 -0.001885
 0.001903
 -0.001921
 0.001939
 -0.001958
 0.001977
 -0.001996
 0.002016
 -0.002037
 0.002057
 -0.002078
 0.002100
 -0.002122
 0.002144
 -0.002167
 0.002191
 -0.002215
 0.002239
 -0.002264
 0.002290
 -0.002316
 0.002343
 -0.002370
 0.002398
 -0.002427
 0.002456
 -0.002486
 0.002517
 -0.002549
 0.002581
 -0.002615
 0.002649
 -0.002684
 0.002720
 -0.002757
 0.002795
 -0.002834
 0.002874
 -0.002916
 0.002958
 -0.003002
 0.003047
 -0.003094
 0.003142
 -0.003191
 0.003242
 -0.003295
 0.003350
 -0.003406
 0.003464
 -0.003524
 0.003587
 -0.003651
 0.003718
 -0.003788
 0.003860
 -0.003935
 0.004013
 -0.004094
 0.004178
 -0.004266
 0.004358
 -0.004454
 0.004554
 -0.004659
 0.004768
 -0.004883
 0.005004
 -0.005130
 0.005264
 -0.005404
 0.005552
 -0.005708
 0.005874
 -0.006049
 0.006235
 -0.006433
 0.006644
 -0.006870
 0.007111
 -0.007369
 0.007647
 -0.007947
 0.008272
 -0.008624
 0.009007
 -0.009426
 0.009886
 -0.010393
 0.010955
 -0.011581
 0.012283
 -0.013076
 0.013978
 -0.015014
 0.016216
 -0.017627
 0.019308
 -0.021342
 0.023856
 -0.027042
 0.031211
 -0.036902
 0.045137
 -0.058124
 0.081682
 -0.138078
 0.589459
 0.589520
 -0.138078
 0.081682
 -0.058124
 0.045137
 -0.036902
 0.031211
 -0.027042
 0.023856
 -0.021342
 0.019308
 -0.017627
 0.016216
 -0.015014
 0.013978
 -0.013076
 0.012283
 -0.011581
 0.010955
 -0.010393
 0.009886
 -0.009426
 0.009007
 -0.008624
 0.008272
 -0.007947
 0.007647
 -0.007369
 0.007111
 -0.006870
 0.006644
 -0.006433
 0.006235
 -0.006049
 0.005874
 -0.005708
 0.005552
 -0.005404
 0.005264
 -0.005130
 0.005004
 -0.004883
 0.004768
 -0.004659
 0.004554
 -0.004454
 0.004358
 -0.004266
 0.004178
 -0.004094
 0.004013
 -0.003935
 0.003860
 -0.003788
 0.003718
 -0.003651
 0.003587
 -0.003524
 0.003464
 -0.003406
 0.003350
 -0.003295
 0.003242
 -0.003191
 0.003142
 -0.003094
 0.003047
 -0.003002
 0.002958
 -0.002916
 0.002874
 -0.002834
 0.002795
 -0.002757
 0.002720
 -0.002684
 0.002649
 -0.002615
 0.002581
 -0.002549
 0.002517
 -0.002486
 0.002456
 -0.002427
 0.002398
 -0.002370
 0.002343
 -0.002316
 0.002290
 -0.002264
 0.002239
 -0.002215
 0.002191
 -0.002167
 0.002144
 -0.002122
 0.002100
 -0.002078
 0.002057
 -0.002037
 0.002016
 -0.001996
 0.001977
 -0.001958
 0.001939
 -0.001921
 0.001903
 -0.001885
 0.001868
 -0.001851
 0.001834
 -0.001817
 0.001801
 -0.001785
 0.001770
 -0.001754
 0.001739
 -0.001725
 0.001710
 -0.001696
 0.001682
 -0.001668
 0.001654
 -0.001641
 0.001628
 -0.001615
 0.001602
 -0.001589
 0.001577
 -0.001565
 0.001553
 -0.001541
 0.001529
 -0.001518
 0.001507
 -0.001496
 0.001485
 -0.001474
 0.001463
 -0.001453
 0.001442
 -0.001432
 0.001422
 -0.001412
 0.001402
 -0.001393
 0.001383
 -0.001374
 0.001365
 -0.001355
 0.001346
 -0.001338
 0.001329
 -0.001320
 0.001312
 -0.001303
 0.001295
 -0.001287
 0.001279
 -0.001270
 0.001263
 -0.001255
 0.001247
 -0.001239
 0.001232
 -0.001224
 0.001217
 -0.001210
 0.001203
 -0.001196
 0.001189
 -0.001182
 0.001175
 -0.001168
 0.001161
 -0.001155
 0.001148
 -0.001142
 0.001135
 -0.001129
 0.001123
 -0.001116
 0.001110
 -0.001104
 0.001098
 -0.001092
 0.001087
 -0.001081
 0.001075
 -0.001069
 0.001064
 -0.001058
 0.001053
 -0.001047
 0.001042
 -0.001037
 0.001031
 -0.001026
 0.001021
 -0.001016
 0.001011
 -0.001006
 0.001001
 ];
  nI = 203;
end
if regu==2
  I = [ 0.001007
 -0.001014
 0.001021
 -0.001028
 0.001035
 -0.001042
 0.001049
 -0.001057
 0.001064
 -0.001072
 0.001079
 -0.001087
 0.001095
 -0.001103
 0.001111
 -0.001119
 0.001127
 -0.001136
 0.001144
 -0.001153
 0.001162
 -0.001171
 0.001180
 -0.001189
 0.001199
 -0.001208
 0.001218
 -0.001228
 0.001238
 -0.001248
 0.001258
 -0.001269
 0.001280
 -0.001290
 0.001301
 -0.001313
 0.001324
 -0.001336
 0.001348
 -0.001360
 0.001372
 -0.001385
 0.001397
 -0.001410
 0.001424
 -0.001437
 0.001451
 -0.001465
 0.001479
 -0.001494
 0.001509
 -0.001524
 0.001539
 -0.001555
 0.001571
 -0.001588
 0.001604
 -0.001622
 0.001639
 -0.001657
 0.001675
 -0.001694
 0.001713
 -0.001733
 0.001753
 -0.001773
 0.001794
 -0.001816
 0.001838
 -0.001860
 0.001883
 -0.001907
 0.001931
 -0.001956
 0.001982
 -0.002008
 0.002035
 -0.002063
 0.002091
 -0.002120
 0.002150
 -0.002181
 0.002213
 -0.002246
 0.002280
 -0.002315
 0.002350
 -0.002387
 0.002426
 -0.002465
 0.002506
 -0.002548
 0.002591
 -0.002637
 0.002683
 -0.002732
 0.002782
 -0.002834
 0.002888
 -0.002944
 0.003002
 -0.003063
 0.003126
 -0.003191
 0.003260
 -0.003332
 0.003406
 -0.003485
 0.003567
 -0.003653
 0.003743
 -0.003838
 0.003937
 -0.004042
 0.004153
 -0.004270
 0.004393
 -0.004525
 0.004664
 -0.004812
 0.004969
 -0.005138
 0.005318
 -0.005511
 0.005719
 -0.005943
 0.006186
 -0.006449
 0.006735
 -0.007048
 0.007392
 -0.007771
 0.008190
 -0.008658
 0.009182
 -0.009774
 0.010448
 -0.011221
 0.012118
 -0.013172
 0.014425
 -0.015943
 0.017818
 -0.020194
 0.023303
 -0.027549
 0.033708
 -0.043510
 0.062551
 -0.161059
 0.812359
 0.377953
 -0.103501
 0.061373
 -0.043660
 0.033889
 -0.027694
 0.023414
 -0.020281
 0.017888
 -0.016000
 0.014472
 -0.013211
 0.012152
 -0.011251
 0.010473
 -0.009797
 0.009202
 -0.008676
 0.008206
 -0.007785
 0.007405
 -0.007060
 0.006746
 -0.006458
 0.006195
 -0.005952
 0.005727
 -0.005518
 0.005325
 -0.005144
 0.004975
 -0.004817
 0.004669
 -0.004529
 0.004398
 -0.004274
 0.004157
 -0.004046
 0.003941
 -0.003841
 0.003746
 -0.003656
 0.003570
 -0.003488
 0.003409
 -0.003334
 0.003263
 -0.003194
 0.003128
 -0.003065
 0.003004
 -0.002946
 0.002890
 -0.002836
 0.002783
 -0.002733
 0.002685
 -0.002638
 0.002593
 -0.002549
 0.002507
 -0.002467
 0.002427
 -0.002389
 0.002352
 -0.002316
 0.002281
 -0.002247
 0.002214
 -0.002183
 0.002152
 -0.002121
 0.002092
 -0.002064
 0.002036
 -0.002009
 0.001983
 -0.001957
 0.001932
 -0.001908
 0.001884
 -0.001861
 0.001839
 -0.001817
 0.001795
 -0.001774
 0.001754
 -0.001733
 0.001714
 -0.001695
 0.001676
 -0.001658
 0.001640
 -0.001622
 0.001605
 -0.001588
 0.001572
 -0.001556
 0.001540
 -0.001524
 0.001509
 -0.001494
 0.001480
 -0.001465
 0.001451
 -0.001438
 0.001424
 -0.001411
 0.001398
 -0.001385
 0.001373
 -0.001360
 0.001348
 -0.001336
 0.001325
 -0.001313
 0.001302
 -0.001291
 0.001280
 -0.001269
 0.001259
 -0.001248
 0.001238
 -0.001228
 0.001218
 -0.001209
 0.001199
 -0.001190
 0.001180
 -0.001171
 0.001162
 -0.001153
 0.001145
 -0.001136
 0.001128
 -0.001119
 0.001111
 -0.001103
 0.001095
 -0.001087
 0.001079
 -0.001072
 0.001064
 -0.001057
 0.001050
 -0.001042
 0.001035
 -0.001028
 0.001021
 -0.001014
 0.001008
 -0.001001
 ];
  nI = 152;
end
if regu==3
  I = [ 0.001003
 -0.001208
 0.001486
 -0.001877
 0.002450
 -0.003342
 0.004846
 -0.007686
 0.013983
 -0.018320
 -0.052992
 0.930205
 0.151315
 -0.027005
 0.011595
 -0.006443
 0.004092
 -0.002823
 0.002061
 -0.001567
 0.001230
 -0.000989
 0.000811
 -0.000677
 0.000572
 ];
  nI = 13;
end
if regu==4
  I = [ 0.001017
 -0.001024
 0.001031
 -0.001038
 0.001045
 -0.001052
 0.001059
 -0.001066
 0.001074
 -0.001081
 0.001089
 -0.001097
 0.001105
 -0.001113
 0.001121
 -0.001129
 0.001137
 -0.001146
 0.001154
 -0.001163
 0.001172
 -0.001181
 0.001190
 -0.001199
 0.001208
 -0.001218
 0.001228
 -0.001237
 0.001247
 -0.001258
 0.001268
 -0.001278
 0.001289
 -0.001300
 0.001311
 -0.001322
 0.001334
 -0.001345
 0.001357
 -0.001369
 0.001381
 -0.001394
 0.001407
 -0.001420
 0.001433
 -0.001446
 0.001460
 -0.001474
 0.001488
 -0.001502
 0.001517
 -0.001532
 0.001548
 -0.001563
 0.001579
 -0.001596
 0.001612
 -0.001629
 0.001647
 -0.001664
 0.001683
 -0.001701
 0.001720
 -0.001739
 0.001759
 -0.001780
 0.001800
 -0.001822
 0.001843
 -0.001866
 0.001888
 -0.001912
 0.001936
 -0.001960
 0.001986
 -0.002011
 0.002038
 -0.002065
 0.002093
 -0.002122
 0.002152
 -0.002182
 0.002213
 -0.002246
 0.002279
 -0.002313
 0.002348
 -0.002384
 0.002422
 -0.002460
 0.002500
 -0.002541
 0.002584
 -0.002628
 0.002673
 -0.002720
 0.002769
 -0.002820
 0.002872
 -0.002927
 0.002983
 -0.003042
 0.003103
 -0.003167
 0.003233
 -0.003302
 0.003375
 -0.003450
 0.003529
 -0.003611
 0.003698
 -0.003789
 0.003884
 -0.003984
 0.004090
 -0.004201
 0.004318
 -0.004443
 0.004574
 -0.004714
 0.004862
 -0.005021
 0.005189
 -0.005370
 0.005563
 -0.005771
 0.005995
 -0.006237
 0.006500
 -0.006786
 0.007097
 -0.007439
 0.007816
 -0.008232
 0.008696
 -0.009215
 0.009799
 -0.010463
 0.011223
 -0.012102
 0.013131
 -0.014350
 0.015819
 -0.017624
 0.019892
 -0.022832
 0.026795
 -0.032432
 0.041115
 -0.056360
 0.085847
 -0.135367
 0.158052
 0.916228
 -0.013877
 0.041053
 -0.034280
 0.028496
 -0.024213
 0.021000
 -0.018520
 0.016556
 -0.014964
 0.013649
 -0.012545
 0.011606
 -0.010797
 0.010093
 -0.009475
 0.008928
 -0.008440
 0.008003
 -0.007609
 0.007252
 -0.006927
 0.006630
 -0.006357
 0.006106
 -0.005874
 0.005658
 -0.005459
 0.005272
 -0.005098
 0.004935
 -0.004782
 0.004639
 -0.004503
 0.004376
 -0.004255
 0.004141
 -0.004033
 0.003930
 -0.003833
 0.003740
 -0.003651
 0.003567
 -0.003487
 0.003410
 -0.003336
 0.003265
 -0.003198
 0.003133
 -0.003070
 0.003011
 -0.002953
 0.002898
 -0.002844
 0.002793
 -0.002743
 0.002695
 -0.002649
 0.002604
 -0.002561
 0.002519
 -0.002479
 0.002440
 -0.002402
 0.002365
 -0.002329
 0.002295
 -0.002261
 0.002228
 -0.002197
 0.002166
 -0.002136
 0.002107
 -0.002078
 0.002051
 -0.002024
 0.001998
 -0.001972
 0.001947
 -0.001923
 0.001899
 -0.001876
 0.001854
 -0.001832
 0.001810
 -0.001789
 0.001769
 -0.001749
 0.001729
 -0.001710
 0.001691
 -0.001673