[Emad Shehata]

Dear Gosia
There is no official command in Stata to estimate Cochrane-Orcutt via MLE

[Emad Shehata]

I will prepare example for estimating Cochrane-Orcutt via MLE

[Eric de Souza]

Re your reply at #9: this is not what you wanted because it does take into account that the residuals are estimated and not observed.
The NLS method in #10 is preferable because it jointly estimates the beta coefficients and rho.

There was a typo in my comment in #11. I should have been "does NOT take into account".
Emad Shehata in #12 saw it and replied to what I had meant to type.
This correction is just for the record.

[Emad Shehata]

Dear Eric
No problem, I noticed that
You are welcome

[Eric de Souza]

Re: MLE, you could use -arima-. It does MLE, I think, but have no time to check now.
webuse lutkepohl2
arima ln_consump ln_inc, ar(1)
Compare with
prais ln_consump ln_inc
This is just for illustration purposes

[Emad Shehata]

Not ARIMA
arima command in Stata deal with all observations and includes the Jacobian term ; i.e, AR(1) = log(1-Rho^2),
But Cochrane-Orcutt method drops the observations of AR(i) order.

Also ARIMA differ from Prais-Winsten estimation as in your example.

[Emad Shehata]

. webuse lutkepohl2
(Quarterly SA West German macro data, Bil DM, from Lutkepohl 1993 Table E.1)

.
.  arima ln_consump ln_inc, ar(1)

(setting optimization to BHHH)
Iteration 0:   log likelihood =  288.57985 
Iteration 1:   log likelihood =  288.78449 
Iteration 2:   log likelihood =  288.80277 
Iteration 3:   log likelihood =  288.80834 
Iteration 4:   log likelihood =  288.80992 
(switching optimization to BFGS)
Iteration 5:   log likelihood =  288.81096 
Iteration 6:   log likelihood =  288.81273 
Iteration 7:   log likelihood =  288.81278 
Iteration 8:   log likelihood =  288.81279 

ARIMA regression

Sample:  1960q1 - 1982q4                        Number of obs      =        92
                                                Wald chi2(2)       =  18775.60
Log likelihood =  288.8128                      Prob > chi2        =    0.0000

------------------------------------------------------------------------------
             |                 OPG
  ln_consump |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
ln_consump   |
      ln_inc |   .9640667   .0070389   136.96   0.000     .9502707    .9778628
       _cons |   .1130424   .0483919     2.34   0.019     .0181959    .2078888
-------------+----------------------------------------------------------------
ARMA         |
          ar |
         L1. |   .7404788   .0748837     9.89   0.000     .5937094    .8872482
-------------+----------------------------------------------------------------
      /sigma |   .0104356   .0007577    13.77   0.000     .0089506    .0119207
------------------------------------------------------------------------------
.
.  prais ln_consump ln_inc

Iteration 0:  rho = 0.0000
Iteration 1:  rho = 0.7160
Iteration 2:  rho = 0.7274
Iteration 3:  rho = 0.7285
Iteration 4:  rho = 0.7286
Iteration 5:  rho = 0.7286
Iteration 6:  rho = 0.7286
Iteration 7:  rho = 0.7286

Prais-Winsten AR(1) regression -- iterated estimates

      Source |       SS       df       MS              Number of obs =      92
-------------+------------------------------           F(  1,    90) =60216.35
       Model |  6.70811142     1  6.70811142           Prob > F      =  0.0000
    Residual |  .010026015    90    .0001114           R-squared     =  0.9985
-------------+------------------------------           Adj R-squared =  0.9985
       Total |  6.71813743    91  .073825686           Root MSE      =  .01055

------------------------------------------------------------------------------
  ln_consump |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      ln_inc |   .9643447     .00689   139.96   0.000     .9506565    .9780328
       _cons |   .1110111   .0488456     2.27   0.025     .0139707    .2080515
-------------+----------------------------------------------------------------
         rho |   .7286484
------------------------------------------------------------------------------
Durbin-Watson statistic (original)    0.534703
Durbin-Watson statistic (transformed) 2.435227

[Emad Shehata]

You can check, not exactly the same results

[Emad Shehata]

you can check here
http://www.statalist.org/forums/foru...utt-regression