Estimating an ARMA(p,q) with a trend

[John Andrews]

Dear all,

I want to estimate a general stationary and invertible ARMA(p,q) model with a time trend (deterministic trend)

Is that possible.

The ARIMA function does not allow for that.


Best

[Joro Kolev]

The -arima- command does allow for what you want. The syntax diagram is

arima depvar [indepvars], ar(numlist) ma(numlist)

Generate your trend variable, and put it in the place of the [indepvars].

Like this:

. webuse wpi1, clear

. arima D.wpi t, ar(1) ma(1) nolog

ARIMA regression

Sample:  1960q2 - 1990q4                        Number of obs     =        123
                                                Wald chi2(3)      =     315.17
Log likelihood = -133.9807                      Prob > chi2       =     0.0000

------------------------------------------------------------------------------
             |                 OPG
       D.wpi |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
wpi          |
           t |   .0110271   .0116397     0.95   0.343    -.0117863    .0338405
       _cons |   .0553015   1.123903     0.05   0.961    -2.147507     2.25811
-------------+----------------------------------------------------------------
ARMA         |
          ar |
         L1. |   .8416682   .0638227    13.19   0.000     .7165781    .9667584
             |
          ma |
         L1. |  -.3917285   .1110694    -3.53   0.000    -.6094206   -.1740364
-------------+----------------------------------------------------------------
      /sigma |   .7174407   .0357831    20.05   0.000     .6473071    .7875743
------------------------------------------------------------------------------
Note: The test of the variance against zero is one sided, and the two-sided
      confidence interval is truncated at zero.

.

[John Andrews]

Many thanks!