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


From   Robert A Yaffee <[email protected]>
To   [email protected]
Subject   Re: st: A cry for help on ARMA with weak autocorrelation
Date   Thu, 06 May 2010 03:33:04 -0400

Dmytro,

  Tirthankar may be correct if you are looking for variations in 
volatility.  There may also be variations in kurtosis and skewness
that could be examined with higher order (power GARCH models)
capable of extracting the signal.
  If you are restricted to lower order processes, white noise might
suggest that a prior filtering took place or that you will have to
await the diminution of the wind to hear the whistle.
  Perhaps an asymmetric power garch that Stata has might be
of use.
       Regards,
    -  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 <[email protected]>
Date: Wednesday, May 5, 2010 8:37 pm
Subject: Re: st: A cry for help on ARMA with weak autocorrelation
To: [email protected]


> 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 <[email protected]>:
> > 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 <[email protected]>
> > Date: Wednesday, May 5, 2010 2:50 pm
> > Subject: st: A cry for help on ARMA with weak autocorrelation
> > To: [email protected]
> >
> >
> >> 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
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> >> -.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
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> >> -.0007591
> >> -.0114279
> >> -.0122776
> >> .0217314
> >> .016614
> >> -.0089483
> >> .0057192
> >> .000289
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> >> .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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