I am trying to estimate an intervention model with the ARIMA command where
the intervention impact is gradual (either pulse-decay or gradual
accumulation).
The equation has the form:
Yt=(omega*It)/(1-deltaB) + Noise
Where It is the intervention variable, B is the back-operator and noise
represents some ARIMA process.
As long as the Noise component does not have an ar(1) component, I would
think you could just estimate delta with the coefficient on yt-1. But if
there is an ar(1) component, lets say
Yt=(omega*It)/(1-deltaB) + psiYt-1 + at
can you manipulate the equation, such that:
(Yt- psiYt-1)(1- deltaB)=(omega*It) + at*(1-deltaB)
Yt- deltaYt- psiYt-1 + psi*delta*Yt-2 = (omega*It) + at - delta*at-t
Yt- (delta+psi)Yt-1 + psi*delta*Yt-2 = (omega*It) + at - delta*at-t
Yt= (delta+psi)Yt-1 - psi*delta*Yt-2 + (omega*It) + at - delta*at-t
?
Thus typing
arima y I, ar(1 2) ma(1)
would give you the delta coefficient on the ma1 term and you could then
calculate psi
However, this does not seem to work in practice. I know RATS and SAS have
programs to compute delta, but I do not have access to those user-manuals in
order to figure out how they are estimating it (and then implement that in
STATA).
Any help on where I have gone astray would be greatly appreciated.
Thanks in advance for your time.
-Mike
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