arimasoc vs arima -- different results

[Alex Tekin]

Dear All,

I have been working with some time-series data (please refer to the attached spreadsheet). I utilized the code below to fit an ARMA(1,2) model to the Y series. However, upon using arimasoc, it's evident from the output table that the ARMA(1,2) model yields different log-likelihood and information criteria values.

I suspect that there might be an error on my end, or perhaps the two commands employ different convergence techniques. Could you please assist me in identifying the discrepancy, or advise if there are default options I should utilize to ensure consistency in the results obtained from the two commands? Thank you for your assistance. (The code is provided below.)

clear

gen Time = mofd(Date)

format Time %tmMonYY

drop Date

gen t = _n

tsset t

arima Y, ar(1) ma(2) 

estat ic

arimasoc Y, maxar(2) maxma(2)

[Andrew Musau]

For lag orders greater or equal to 2 (for both the AR and MA components), the model that arimasoc estimates includes all lower level lags.

webuse usmacro, clear
arimasoc ogap, maxar(2) maxma(2)
arima ogap, ar(1) ma(1/2)

Res.:

. arimasoc ogap, maxar(2) maxma(2)
Fitting models (9): ......... done

Lag-order selection criteria

Sample: 1954q3 thru 2010q4                       Number of obs = 226
--------------------------------------------------------------------
       Model |        LL         df        AIC        BIC       HQIC
-------------+------------------------------------------------------
   ARMA(0,0) | -549.4036          2   1102.807   1109.648   1105.568
   ARMA(0,1) | -435.0753          3   876.1507   886.4123   880.2919
   ARMA(0,2) |  -361.249          4   730.4981   744.1802   736.0196
   ARMA(1,0) | -292.3313          3   590.6625   600.9241   594.8037
   ARMA(1,1) | -281.5762          4   571.1524   584.8345   576.6739
   ARMA(1,2) | -275.3697          5   560.7395   577.8422   567.6414
   ARMA(2,0) | -276.5956          4   561.1912   574.8733   566.7127
   ARMA(2,1) | -273.9052          5   557.8104   574.9131   564.7123
   ARMA(2,2) | -273.2799          6   558.5599   579.0831   566.8422
--------------------------------------------------------------------
Selected (max) LL:   ARMA(2,2)
Selected (min) AIC:  ARMA(2,1)
Selected (min) BIC:  ARMA(2,0)
Selected (min) HQIC: ARMA(2,1)

.
. arima ogap, ar(1) ma(1/2)

(setting optimization to BHHH)
Iteration 0:  Log likelihood = -278.31258  
Iteration 1:  Log likelihood = -276.00767  
Iteration 2:  Log likelihood = -275.50366  
Iteration 3:  Log likelihood = -275.40699  
Iteration 4:  Log likelihood = -275.38101  
(switching optimization to BFGS)
Iteration 5:  Log likelihood = -275.37312  
Iteration 6:  Log likelihood = -275.36975  
Iteration 7:  Log likelihood = -275.36974  

ARIMA regression

Sample: 1954q3 thru 2010q4                      Number of obs     =        226
                                                Wald chi2(3)      =    1135.72
Log likelihood = -275.3697                      Prob > chi2       =     0.0000

------------------------------------------------------------------------------
             |                 OPG
        ogap | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
ogap         |
       _cons |   -.800509   .8780935    -0.91   0.362    -2.521541    .9205226
-------------+----------------------------------------------------------------
ARMA         |
          ar |
         L1. |   .8990366   .0355157    25.31   0.000     .8294272    .9686461
             |
          ma |
         L1. |   .3263841   .0623434     5.24   0.000     .2041932    .4485749
         L2. |   .2254193   .0613523     3.67   0.000     .1051709    .3456677
-------------+----------------------------------------------------------------
      /sigma |   .8136397    .029494    27.59   0.000     .7558325    .8714469
------------------------------------------------------------------------------
Note: The test of the variance against zero is one sided, and the two-sided
      confidence interval is truncated at zero.

.

[Alex Tekin]

Thank you Andrew. It seems my mistake was that I only included 1 lag for MA term, as opposed to both. Need to be more careful, thanks again!