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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/