On Wed, 27 Oct 2010, [iso-8859-1] Gústaf Steingrímsson wrote:
Maybe I was unclear about my problem. I was using standard
non-seasonal ARIMA(1,1,1) model which should be on the form:
Y^(t) = c + Y(t-1) + Phi*(Y(t-1)-Y(t-2)) + theta*e(t-1)
I got parameters from Gretl for c, Phi and theta. I also got
time series for Y(t) and Y^(t) for many values of t's.
Please see the discussion in the Gretl User's Guide, The "Time
series models" chapter, around equations (21.4) and (21.5) in
particular. There are various ways of formulating AR(I)MA
models, and you have to be aware which one gretl is using.
If you're using exact ML, then in the equation you give above,
you'll need to replace c with c*(1-phi). That should give you
something very close to what gretl computes automatically, if not
identical. There may also be a difference in the treatment of
initial values; I'll have to look into that.