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Re: st: what is SIGMA2 _const in arima

From (Vince Wiggins, StataCorp)
Subject   Re: st: what is SIGMA2 _const in arima
Date   Thu, 24 Aug 2006 14:47:19 -0500

Olga Gorbachev Melloni <> asks,

> I am trying to estimate a model, in which errors follow an MA(1). I
> have panel data, and I assume that for each cohort, coefficients are
> the same.  I ran:
> arima y x if cohort==1935, ma(1) condition
>  [...]
> 2. When trying to predict the errors or the predicted values, I got
> an error message saying that the sample cannot include panels.
> Is there a way to get the predicted values and/or white-noise
> errors?

Bob Yaffee <> answered Olga's first question, which I did
not repeat above.

Olga has uncovered a buglet in -arima-.  No results are compromised, some
things just cannot be done directly by -arima- when estimating with the
-conditional- method, but read on, there is a work around.

This is happening because the unconditional maximum likelihood estimation
and prediction method used by -arima- is not up to panel data.  Unlike the
conditional estimation method, it cannot restart itself at the beginning of
each panel.  -arima- is at its heart an unconditional ML estimator, both in
implementation and as documented in the Methods and Formulas of [TS] arima.
To obtain conditional estimates -arima- actually calls through to -arch-,
which is at its heart a conditional ML estimator.  -arima- then presents the
-arch- results as its own.  

So long as you do not have panels, this is fine.  With a single time-series,
-arima- can predict using the unconditional method of prediction, and unlike
-arch-, can gracefully handle maintaining information over any time gaps
during a prediction.  (-arch- simply restarts at any gap.  That is fine
asymptotically, but what -arima- does is a bit more efficient.)  For that
reason, it is usually best to let -arima- predict using its unconditional
method, even when the estimates come from the -arch- conditional estimator.

We have not yet decided how to handle this in -arima-.  It's not clear that
grafting the unconditional estimator into -arima- was the best approach,
though it is unlikely that Olga and others would have found it for ARIMA
modeling had it been left only in -arch-.

Regardless, until we have decided how to proceed, Olga can get her predictions
by using -arch- in place of -arima-.  Just use -arch- with only ARIMA terms
and without any ARCH terms.  The syntax is similar and she need not specify
-conditional- because that is the only estimator -arch- knows.  The estimation
results will be identical to those obtained with -arima, conditional- and
-predict- will work on panel data after -arch-.

-- Vince

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