## Fitted Values from ARMA

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### Fitted Values from ARMA

Hello,
I am trying to compute fitted values from an estimated ARMA model, but my results are not correct.

boxjenk(constant,ar=1,ma=1,inputs=0,iter=1000,define=equation) dsp 1995:1 2008:12 res1
set fitted = 0.0
do t=1995:3,2008:12
com fitted(t)= %beta(1) + %beta(2)*dsp(t-1) + %beta(3)*res1(t-1)
end do

set fit = dsp-res1

The difference between fitted and fit is always equal to -1.42, starting from 1995:3 onwards.
Am I computing fitted wrong?
John_Val

Posts: 25
Joined: Sun May 17, 2009 2:18 pm

### Re: Fitted Values from ARMA

The constant in the BOXJENK formulation is the process mean, not the intercept in an ARMA equation. To convert that into the form you're using, the equivalent representation is:

y-%beta(1) = %beta(2)*(y{1}-%beta(1))+eps+%beta(3)*eps{1}

or

y = %beta(1)*(1-%beta(2))+%beta(2)*y{1}+eps+%beta(3)*eps{1}

So instead of using %beta(1) as the intercept, use %beta(1)*(1-%beta(2)).

BTW, the PRJ instruction will work after a BOXJENK. You could just do

prj fitted 1995:3 2008:12