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Re: st: A cry for help on ARMA with weak autocorrelation


From   Robert A Yaffee <bob.yaffee@nyu.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: A cry for help on ARMA with weak autocorrelation
Date   Thu, 06 May 2010 03:57:14 -0400

a bilinear model with a negative interaction effect that could suppress the significance of the main p and q effects?
   Robert
    
    .

Robert A. Yaffee, Ph.D.
Research Professor
Silver School of Social Work
New York University

Biosketch: http://homepages.nyu.edu/~ray1/Biosketch2009.pdf

CV:  http://homepages.nyu.edu/~ray1/vita.pdf

----- Original Message -----
From: Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com>
Date: Wednesday, May 5, 2010 8:37 pm
Subject: Re: st: A cry for help on ARMA with weak autocorrelation
To: statalist@hsphsun2.harvard.edu


> This is symptomatic of GARCH effects:
> ****************************************
> clear*
> input dmytro
> -.0090714
> .0218658
> -.0268755
> .0024567
> -.056356
> .0046611
> .0136881
> -.0091224
> .0054574
> -.0334902
> .0212493
> .0597358
> -.0207405
> .0116024
> -.01581
> -.0096569
> .0243721
> -.0002346
> -.0107546
> -.0070105
> .0029306
> .0054045
> .0222607
> .0032482
> .033515
> -.0261011
> -.0244341
> -.0354443
> .0121222
> .0120258
> -.0312228
> .0112433
> .0132771
> .0068617
> .0016813
> .0044956
> -.0182991
> -.0232587
> .0172067
> -.0174499
> -.0107841
> .019073
> -.0025773
> -.0036931
> .0090313
> .0116596
> -.0042143
> -.01231
> -.0116882
> -.0226994
> -.0131874
> .007977
> -.05966
> -.0327191
> .0383449
> -.0062823
> .0268879
> .0207028
> .0112748
> -.0086665
> .0050945
> .0044184
> -.0026326
> -.0121818
> .0221472
> -.0393658
> -.0099735
> -.0052757
> -.0292039
> .0091033
> -.0250168
> -.0004563
> .027513
> -.021317
> -.0123415
> .0211291
> -.0212989
> -.0510502
> -.0655146
> -.079906
> .0951033
> .0257664
> .0244412
> -.0225444
> .0309162
> -.0119662
> .026412
> .0141501
> .0005832
> -.016212
> .0151157
> -.0394745
> .0161915
> .0154595
> .0185943
> -.0217462
> -.0145679
> .0094967
> -.0019608
> -.0120802
> .0098996
> -.0255461
> .0237536
> .0244961
> .0004768
> -.0053186
> .0042987
> -.0058708
> -.0125189
> .0147271
> -.015285
> .0082312
> -.005342
> .0082111
> -.009253
> -.01542
> -.0301108
> -.0584188
> -.0084252
> .0072241
> -.0106797
> -.0837865
> -.0313945
> -.0242662
> .0136309
> .0507717
> .0040598
> .0164299
> -.0355163
> -.0292273
> -.0222354
> -.0383153
> .0077167
> -.027843
> .0302272
> .043324
> -.015892
> -.0109243
> .0109863
> .0109072
> .019958
> -.0000401
> -.0357337
> -.0340881
> .0012894
> -.0131588
> .0413365
> -.0064459
> -.0354757
> -.0530305
> -.0156755
> .0089307
> .0016389
> .0281925
> -.0176201
> -.0430017
> .0250711
> .0661936
> -.0374131
> .0256433
> .0016427
> .0218129
> -.0025196
> .0220518
> .0072665
> .0238113
> -.0167165
> .018806
> .0283427
> -.0035315
> .0055637
> -.0215859
> -.0089717
> .0117569
> .0052133
> .0135822
> -.0033212
> .0096278
> .0253091
> -.0016627
> -.0127578
> .0227208
> -.0063972
> .006104
> -.0260959
> .0258164
> .0116844
> .0090237
> -.0258517
> .0119371
> .0197902
> .0026026
> -.0191984
> .0068007
> .0063615
> -.0058165
> .0127311
> .0071321
> .0144997
> -.0052276
> .0084658
> -.0059638
> -.0135465
> .0038967
> .0044174
> .0219884
> -.0048823
> .0122457
> -.0176673
> -.009655
> -.0123987
> .0232635
> .004787
> .0067487
> .0085082
> -.0185409
> -.0008988
> -.0144238
> -.002049
> .0013633
> .0054221
> .0073538
> .0035315
> .0001254
> -.0163507
> -.0059991
> -.0107484
> -.0047631
> .0170636
> -.0178342
> -.0078974
> .0154333
> .0259404
> .0131297
> .0016165
> .0096965
> -.0041585
> .0171118
> .0085721
> -.0161495
> -.0008807
> .0023966
> .0251546
> .0112433
> -.0052514
> -.0034738
> .0024099
> -.0090661
> .0025158
> .0200453
> .0044689
> .0076365
> -.0037117
> -.0016336
> .0056829
> .022727
> .0188918
> .0005565
> -.0095177
> .0065622
> -.0097098
> -.0106926
> -.0022764
> -.0008583
> .0134516
> -.0193677
> -.008615
> -.0148244
> .0210567
> -.0056529
> .0173368
> .0061102
> .00454
> .0065217
> .0098181
> -.0000982
> .0154285
> .0129695
> -.00073
> .0021348
> .0089025
> .0067787
> .0054498
> -.0059829
> -.0127592
> .0177407
> .0060458
> .0085001
> .0001955
> .0115237
> -.021904
> -.0161366
> -.0252199
> .0126491
> .0416818
> .0083432
> .0076814
> .006319
> .0036798
> -.0017376
> .0038514
> .0128078
> .0041885
> .0190792
> -.0025673
> -.0047374
> .0207295
> -.0031738
> .0021157
> .0141172
> .0022464
> -.0001411
> .0059633
> .0192223
> .0063477
> -.0110016
> .0098848
> -.0019283
> .0168991
> -.016264
> .0130329
> -.0294342
> -.0474505
> .0242586
> -.004715
> -.0229926
> -.0079083
> .0155926
> .0242987
> .0081582
> -.0317149
> .0022745
> .0402284
> -.0121889
> -.0115776
> .0160389
> -.0036221
> .013381
> -.0112391
> .0025024
> -.0076647
> .0229626
> .0084715
> .0246611
> -.000844
> .0007362
> -.0011082
> .0119686
> -.0007591
> -.0114279
> -.0122776
> .0217314
> .016614
> -.0089483
> .0057192
> .000289
> .0015287
> .0005388
> -.0017853
> .0141611
> .0119972
> .0053654
> -.0015335
> -.0459242
> .0222826
> -.0173922
> .0336294
> -.004158
> .0146761
> .0085745
> .0027933
> -.0084667
> .0272865
> -.0069933
> .0115929
> -.0105085
> .0153751
> -.0298243
> .0334148
> -.025835
> .0040855
> .0145779
> .0039845
> -.0174904
> -.0595789
> .0040874
> -.0296612
> -.0002079
> .0253992
> .0157719
> -.0175371
> .0108528
> .0232458
> .0005913
> .0209351
> .0197239
> -.0291605
> .0194979
> -.0176277
> -.0376501
> -.0035934
> -.0084867
> .0254431
> .0140886
> -.0237761
> .0064907
> .0073729
> -.0218363
> -.0263119
> -.0443525
> -.0044308
> .0287313
> -.0400453
> .0019059
> .0169611
> .0000362
> -.0302677
> -.0127449
> -.0253201
> .037117
> .0400047
> -.0103674
> .0268259
> .0023079
> .0210543
> .0002432
> .0138454
> -.0347366
> -.0052414
> -.0239954
> -.0180578
> -.0313873
> -.018117
> -.0275869
> -.0278697
> .0277452
> -.0048842
> .0003047
> .0267324
> -.0051508
> .0073652
> .0230937
> -.0676994
> .027998
> -.0175819
> -.0480194
> -.0234528
> -.2254887
> .0186381
> -.050343
> .1131096
> .0031643
> -.0352201
> -.1120925
> .1211257
> -.0579996
> .0575261
> .0037999
> -.0139828
> .0747881
> -.0212183
> -.0686975
> -.0238781
> .0235171
> .0349255
> -.021409
> -.0750003
> -.0129738
> -.0756612
> .0597296
> .0227227
> .0146079
> .0395327
> -.0081658
> .0301604
> .0145698
> .0219765
> .0479522
> -.0284438
> .0047235
> .0110078
> .0070996
> 9.06e-06
> -.0253553
> -.0203786
> -.0011497
> -.0259624
> .059896
> .0423455
> .0072837
> .0299325
> -.0012712
> .0270276
> .0129409
> -.0113106
> .0352964
> .0290713
> -.0188484
> -.0181832
> .0361772
> .0055947
> .0070224
> -.0397735
> .0190506
> .029408
> -.0102329
> end
> g id = _n
> tsset id
> tsline dmytro
> reg dmytro
> estat archlm, lags(1(1)10)
> arch dmytro, arch(1) garch(1)
> ****************************************
> 
> T
> 
> 2010/5/6 Robert A Yaffee <bob.yaffee@nyu.edu>:
> > Dmytro,
> >   It sounds as if you have more noise than signal.  If you cannot
> > decompose that into any signal, you may merely have white noise.
> >   - Robert
> >
> >
> > Robert A. Yaffee, Ph.D.
> > Research Professor
> > Silver School of Social Work
> > New York University
> >
> > Biosketch: http://homepages.nyu.edu/~ray1/Biosketch2009.pdf
> >
> > CV:  http://homepages.nyu.edu/~ray1/vita.pdf
> >
> > ----- Original Message -----
> > From: Dmytro Andriychenko <dmytro@blueyonder.co.uk>
> > Date: Wednesday, May 5, 2010 2:50 pm
> > Subject: st: A cry for help on ARMA with weak autocorrelation
> > To: statalist@hsphsun2.harvard.edu
> >
> >
> >> Dear Statalist,
> >>
> >> I have been recently asked to fit a univariate model for a particular
> >> stationary time series. I thought ARMA will be the obvious choice, 
> but
> >> when
> >> I looked at the autocorrelation within the series, I found that the 
> first
> >> two lags are not significant and the few significant ones are only
> >> marginally so (see corrgram output below).
> >>
> >> I guess I can still do the estimates, but I am very much wondering 
> if
> >> ARMA
> >> is appropriate modeling technique here. Is it even valid? Portmanteau
> >> statistics is not rejecting hypothesis of no autocorrelation and Q 
> stats
> >> suggest marginal significance at lag 3,5 and 7 in the first series.
> >>
> >> The question is:  is it even appropriate to be building ARMA in the
> >> light of
> >> such weak autocorrelation, especially that the first two lags are not
> >> significant? If ARMA is not appropriate, then what can it be?
> >>
> >> If anyone can help me with that, or better still point me towards a
> >> reference that would explain that, I would very much extremely appreciate
> >> that. I have been reading books on econometrics for over a week, 
> but still
> >> cannot conclusively answer the question.
> >>
> >> Thank you,
> >>
> >> Dmytro
> >>
> >>                                           -1       0       1 -1
> >> 0
> >> 1
> >>  LAG       AC       PAC      Q     Prob>Q  [Autocorrelation]  [Partial
> >> Autocor]
> >> ----------------------------------------------------------------------------
> >> ---
> >> 1       -0.0516  -0.0516   1.3555  0.2443          |
> >> |
> >>
> >> 2        0.0574   0.0551   3.0348  0.2193          |
> >> |
> >>
> >> 3       -0.1253  -0.1209   11.062  0.0114         -|
> >> |
> >>
> >> 4       -0.0248  -0.0401   11.377  0.0226          |
> >> |
> >>
> >> 5        0.0887   0.1020   15.417  0.0087          |
> >> |
> >>
> >> 6        0.0809   0.0808   18.785  0.0045          |
> >> |
> >>
> >> 7       -0.1274  -0.1468   27.146  0.0003         -|               
>   -|
> >>
> >> 8        0.0455   0.0491   28.214  0.0004          |
> >> |
> >>
> >> 9       -0.0718  -0.0235   30.882  0.0003          |
> >> |
> >>
> >> 10      -0.0196  -0.0722   31.081  0.0006          |
> >> |
> >>
> >> 11       0.0029  -0.0091   31.085  0.0011          |
> >> |
> >>
> >> 12      -0.0930  -0.0818   35.588  0.0004          |
> >> |
> >>
> >> 13       0.1613   0.1684   49.154  0.0000          |-
> >> |-
> >>
> >> 14      -0.0064  -0.0050   49.176  0.0000          |
> >> |
> >>
> >> 15       0.0465   0.0277   50.305  0.0000          |
> >> |
> >>
> >> 16       0.0520   0.0951   51.726  0.0000          |
> >> |
> >>
> >> 17      -0.0261  -0.0090   52.084  0.0000          |
> >> |
> >>
> >> 18       0.0407   0.0249   52.955  0.0000          |
> >> |
> >>
> >> 19       0.0720   0.0485   55.692  0.0000          |
> >> |
> >>
> >> 20      -0.0093   0.0368   55.738  0.0000          |
> >> |
> >>
> >> 21       0.0882   0.0593   59.865  0.0000          |
> >> |
> >>
> >> 22       0.0209   0.0623   60.098  0.0000          |
> >> |
> >>
> >> 23      -0.0231  -0.0031   60.381  0.0000          |
> >> |
> >>
> >> 24      -0.0112  -0.0256   60.448  0.0001          |
> >> |
> >>
> >> 25      -0.0611  -0.0094   62.445  0.0000          |
> >> |
> >>
> >> 26       0.0820   0.0641   66.046  0.0000          |
> >> |
> >>
> >> 27      -0.0818  -0.1022    69.64  0.0000          |
> >> |
> >>
> >> 28      -0.0372  -0.0531   70.384  0.0000          |
> >> |
> >>
> >> 29      -0.0148   0.0117   70.503  0.0000          |
> >> |
> >>
> >> 30      -0.0195  -0.0182   70.708  0.0000          |
> >> |
> >>
> >> 31       0.0606   0.0384   72.693  0.0000          |
> >> |
> >>
> >> 32       0.0101  -0.0140   72.748  0.0001          |
> >> |
> >>
> >> 33       0.0248   0.0807   73.083  0.0001          |
> >> |
> >>
> >> 34       0.0049  -0.0336   73.096  0.0001          |
> >> |
> >>
> >> 35      -0.0110  -0.0529   73.162  0.0002          |
> >> |
> >>
> >> 36      -0.0420  -0.0467   74.129  0.0002          |
> >> |
> >>
> >> 37       0.0684   0.0485   76.693  0.0001          |
> >> |
> >>
> >> 38       0.0291   0.0632   77.159  0.0002          |
> >> |
> >>
> >> 39       0.0517  -0.0230   78.631  0.0002          |
> >> |
> >>
> >> 40      -0.0336   0.0225   79.255  0.0002          |
> >> |
> >>
> >>
> >>
> >> The values are:
> >>
> >> -.0090714
> >> .0218658
> >> -.0268755
> >> .0024567
> >> -.056356
> >> .0046611
> >> .0136881
> >> -.0091224
> >> .0054574
> >> -.0334902
> >> .0212493
> >> .0597358
> >> -.0207405
> >> .0116024
> >> -.01581
> >> -.0096569
> >> .0243721
> >> -.0002346
> >> -.0107546
> >> -.0070105
> >> .0029306
> >> .0054045
> >> .0222607
> >> .0032482
> >> .033515
> >> -.0261011
> >> -.0244341
> >> -.0354443
> >> .0121222
> >> .0120258
> >> -.0312228
> >> .0112433
> >> .0132771
> >> .0068617
> >> .0016813
> >> .0044956
> >> -.0182991
> >> -.0232587
> >> .0172067
> >> -.0174499
> >> -.0107841
> >> .019073
> >> -.0025773
> >> -.0036931
> >> .0090313
> >> .0116596
> >> -.0042143
> >> -.01231
> >> -.0116882
> >> -.0226994
> >> -.0131874
> >> .007977
> >> -.05966
> >> -.0327191
> >> .0383449
> >> -.0062823
> >> .0268879
> >> .0207028
> >> .0112748
> >> -.0086665
> >> .0050945
> >> .0044184
> >> -.0026326
> >> -.0121818
> >> .0221472
> >> -.0393658
> >> -.0099735
> >> -.0052757
> >> -.0292039
> >> .0091033
> >> -.0250168
> >> -.0004563
> >> .027513
> >> -.021317
> >> -.0123415
> >> .0211291
> >> -.0212989
> >> -.0510502
> >> -.0655146
> >> -.079906
> >> .0951033
> >> .0257664
> >> .0244412
> >> -.0225444
> >> .0309162
> >> -.0119662
> >> .026412
> >> .0141501
> >> .0005832
> >> -.016212
> >> .0151157
> >> -.0394745
> >> .0161915
> >> .0154595
> >> .0185943
> >> -.0217462
> >> -.0145679
> >> .0094967
> >> -.0019608
> >> -.0120802
> >> .0098996
> >> -.0255461
> >> .0237536
> >> .0244961
> >> .0004768
> >> -.0053186
> >> .0042987
> >> -.0058708
> >> -.0125189
> >> .0147271
> >> -.015285
> >> .0082312
> >> -.005342
> >> .0082111
> >> -.009253
> >> -.01542
> >> -.0301108
> >> -.0584188
> >> -.0084252
> >> .0072241
> >> -.0106797
> >> -.0837865
> >> -.0313945
> >> -.0242662
> >> .0136309
> >> .0507717
> >> .0040598
> >> .0164299
> >> -.0355163
> >> -.0292273
> >> -.0222354
> >> -.0383153
> >> .0077167
> >> -.027843
> >> .0302272
> >> .043324
> >> -.015892
> >> -.0109243
> >> .0109863
> >> .0109072
> >> .019958
> >> -.0000401
> >> -.0357337
> >> -.0340881
> >> .0012894
> >> -.0131588
> >> .0413365
> >> -.0064459
> >> -.0354757
> >> -.0530305
> >> -.0156755
> >> .0089307
> >> .0016389
> >> .0281925
> >> -.0176201
> >> -.0430017
> >> .0250711
> >> .0661936
> >> -.0374131
> >> .0256433
> >> .0016427
> >> .0218129
> >> -.0025196
> >> .0220518
> >> .0072665
> >> .0238113
> >> -.0167165
> >> .018806
> >> .0283427
> >> -.0035315
> >> .0055637
> >> -.0215859
> >> -.0089717
> >> .0117569
> >> .0052133
> >> .0135822
> >> -.0033212
> >> .0096278
> >> .0253091
> >> -.0016627
> >> -.0127578
> >> .0227208
> >> -.0063972
> >> .006104
> >> -.0260959
> >> .0258164
> >> .0116844
> >> .0090237
> >> -.0258517
> >> .0119371
> >> .0197902
> >> .0026026
> >> -.0191984
> >> .0068007
> >> .0063615
> >> -.0058165
> >> .0127311
> >> .0071321
> >> .0144997
> >> -.0052276
> >> .0084658
> >> -.0059638
> >> -.0135465
> >> .0038967
> >> .0044174
> >> .0219884
> >> -.0048823
> >> .0122457
> >> -.0176673
> >> -.009655
> >> -.0123987
> >> .0232635
> >> .004787
> >> .0067487
> >> .0085082
> >> -.0185409
> >> -.0008988
> >> -.0144238
> >> -.002049
> >> .0013633
> >> .0054221
> >> .0073538
> >> .0035315
> >> .0001254
> >> -.0163507
> >> -.0059991
> >> -.0107484
> >> -.0047631
> >> .0170636
> >> -.0178342
> >> -.0078974
> >> .0154333
> >> .0259404
> >> .0131297
> >> .0016165
> >> .0096965
> >> -.0041585
> >> .0171118
> >> .0085721
> >> -.0161495
> >> -.0008807
> >> .0023966
> >> .0251546
> >> .0112433
> >> -.0052514
> >> -.0034738
> >> .0024099
> >> -.0090661
> >> .0025158
> >> .0200453
> >> .0044689
> >> .0076365
> >> -.0037117
> >> -.0016336
> >> .0056829
> >> .022727
> >> .0188918
> >> .0005565
> >> -.0095177
> >> .0065622
> >> -.0097098
> >> -.0106926
> >> -.0022764
> >> -.0008583
> >> .0134516
> >> -.0193677
> >> -.008615
> >> -.0148244
> >> .0210567
> >> -.0056529
> >> .0173368
> >> .0061102
> >> .00454
> >> .0065217
> >> .0098181
> >> -.0000982
> >> .0154285
> >> .0129695
> >> -.00073
> >> .0021348
> >> .0089025
> >> .0067787
> >> .0054498
> >> -.0059829
> >> -.0127592
> >> .0177407
> >> .0060458
> >> .0085001
> >> .0001955
> >> .0115237
> >> -.021904
> >> -.0161366
> >> -.0252199
> >> .0126491
> >> .0416818
> >> .0083432
> >> .0076814
> >> .006319
> >> .0036798
> >> -.0017376
> >> .0038514
> >> .0128078
> >> .0041885
> >> .0190792
> >> -.0025673
> >> -.0047374
> >> .0207295
> >> -.0031738
> >> .0021157
> >> .0141172
> >> .0022464
> >> -.0001411
> >> .0059633
> >> .0192223
> >> .0063477
> >> -.0110016
> >> .0098848
> >> -.0019283
> >> .0168991
> >> -.016264
> >> .0130329
> >> -.0294342
> >> -.0474505
> >> .0242586
> >> -.004715
> >> -.0229926
> >> -.0079083
> >> .0155926
> >> .0242987
> >> .0081582
> >> -.0317149
> >> .0022745
> >> .0402284
> >> -.0121889
> >> -.0115776
> >> .0160389
> >> -.0036221
> >> .013381
> >> -.0112391
> >> .0025024
> >> -.0076647
> >> .0229626
> >> .0084715
> >> .0246611
> >> -.000844
> >> .0007362
> >> -.0011082
> >> .0119686
> >> -.0007591
> >> -.0114279
> >> -.0122776
> >> .0217314
> >> .016614
> >> -.0089483
> >> .0057192
> >> .000289
> >> .0015287
> >> .0005388
> >> -.0017853
> >> .0141611
> >> .0119972
> >> .0053654
> >> -.0015335
> >> -.0459242
> >> .0222826
> >> -.0173922
> >> .0336294
> >> -.004158
> >> .0146761
> >> .0085745
> >> .0027933
> >> -.0084667
> >> .0272865
> >> -.0069933
> >> .0115929
> >> -.0105085
> >> .0153751
> >> -.0298243
> >> .0334148
> >> -.025835
> >> .0040855
> >> .0145779
> >> .0039845
> >> -.0174904
> >> -.0595789
> >> .0040874
> >> -.0296612
> >> -.0002079
> >> .0253992
> >> .0157719
> >> -.0175371
> >> .0108528
> >> .0232458
> >> .0005913
> >> .0209351
> >> .0197239
> >> -.0291605
> >> .0194979
> >> -.0176277
> >> -.0376501
> >> -.0035934
> >> -.0084867
> >> .0254431
> >> .0140886
> >> -.0237761
> >> .0064907
> >> .0073729
> >> -.0218363
> >> -.0263119
> >> -.0443525
> >> -.0044308
> >> .0287313
> >> -.0400453
> >> .0019059
> >> .0169611
> >> .0000362
> >> -.0302677
> >> -.0127449
> >> -.0253201
> >> .037117
> >> .0400047
> >> -.0103674
> >> .0268259
> >> .0023079
> >> .0210543
> >> .0002432
> >> .0138454
> >> -.0347366
> >> -.0052414
> >> -.0239954
> >> -.0180578
> >> -.0313873
> >> -.018117
> >> -.0275869
> >> -.0278697
> >> .0277452
> >> -.0048842
> >> .0003047
> >> .0267324
> >> -.0051508
> >> .0073652
> >> .0230937
> >> -.0676994
> >> .027998
> >> -.0175819
> >> -.0480194
> >> -.0234528
> >> -.2254887
> >> .0186381
> >> -.050343
> >> .1131096
> >> .0031643
> >> -.0352201
> >> -.1120925
> >> .1211257
> >> -.0579996
> >> .0575261
> >> .0037999
> >> -.0139828
> >> .0747881
> >> -.0212183
> >> -.0686975
> >> -.0238781
> >> .0235171
> >> .0349255
> >> -.021409
> >> -.0750003
> >> -.0129738
> >> -.0756612
> >> .0597296
> >> .0227227
> >> .0146079
> >> .0395327
> >> -.0081658
> >> .0301604
> >> .0145698
> >> .0219765
> >> .0479522
> >> -.0284438
> >> .0047235
> >> .0110078
> >> .0070996
> >> 9.06e-06
> >> -.0253553
> >> -.0203786
> >> -.0011497
> >> -.0259624
> >> .059896
> >> .0423455
> >> .0072837
> >> .0299325
> >> -.0012712
> >> .0270276
> >> .0129409
> >> -.0113106
> >> .0352964
> >> .0290713
> >> -.0188484
> >> -.0181832
> >> .0361772
> >> .0055947
> >> .0070224
> >> -.0397735
> >> .0190506
> >> .029408
> >> -.0102329
> >>
> >>
> >>
> >> *
> >> *   For searches and help try:
> >> *   http://www.stata.com/help.cgi?search
> >> *   http://www.stata.com/support/statalist/faq
> >> *   http://www.ats.ucla.edu/stat/stata/
> > *
> > *   For searches and help try:
> > *   http://www.stata.com/help.cgi?search
> > *   http://www.stata.com/support/statalist/faq
> > *   http://www.ats.ucla.edu/stat/stata/
> >
> 
> 
> 
> -- 
> To every ω-consistent recursive class κ of formulae there correspond
> recursive class signs r, such that neither v Gen r nor Neg(v Gen r)
> belongs to Flg(κ) (where v is the free variable of r).
> 
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/


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