Andrew,
It is my understanding that Stata uses a state space model to run the ARIMA.
Although state space models can filter the missing observations, the failure to
properly interpolate the missing values will corrupt the ACF and PACF. It may
also impair the significance tests.
In The Statistical Analysis of Missing Data (1987) by Rod Little and Don Rubin, they
recommend using the state space Kalman filter to estimate the missing values (p.165ff).
They also suggest that this may also be done with an EM algorithm, such imputation carries
with it some assumptions--specifically that all of the
unobserved components in the model are properly specified. However, there needs
to be proper filtering of the error variances along with the updating of the estimated level.
Stata uses the Kalman filter updating to for the level in the state vector as well
as to update the variances from the covariance matirx as well.
This may work well for small gaps, but when the gaps constitute sizeable chunks of the
series, your results may be less than adequate. You should not have whole seasons
missing from your sample if you have to model seasonality,for example.
Regards,
Bob Yaffee
----- Original Message -----
From: "Andrew H. Sidman" <[email protected]>
Date: Monday, January 28, 2008 6:40 pm
Subject: st: Question on Estimating ARIMA with Gaps in the Series
To: [email protected]
> Hi all
>
>
>
> I have a time series that has gaps. This variable, for example, has 10
> consecutive periods in which the variable is missing. After tsset, I
> ran the
> following:
>
>
>
> . arima overall2 in 277/320, ar(1)
>
>
>
> I get the following note before the output:
>
>
>
> Number of gaps in sample: 1
>
> (note: filtering over missing observations)
>
>
>
> Does anyone know how Stata filters over the missing observations?
> Also, is
> the filtering method the same regardless of how the missing
> observations are
> structured? For example, does the procedure change if instead of 1
> gap of
> 10 periods, I had 10 gaps of 1 period each? I have looked in several
> places
> and must be missing something.
>
>
>
> Thanks for the help.
>
>
>
> Andrew H. Sidman
>
> Assistant Professor
>
> Department of Government
>
> John Jay College of Criminal Justice
>
> The City University of New York
>
> 445 W. 59th Street
>
> New York, NY 10019
>
> Phone: (646) 557-4613
>
> Fax: (212) 237-8245
>
> Email: [email protected]
>
> Web: www.geocities.com/andrewsidman
>
>
>
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