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st: Determining correct lag structure for GARCH model


From   Chad Atkinson <chad.atkinson@wright.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: Determining correct lag structure for GARCH model
Date   Fri, 23 Feb 2007 11:57:40 -0500

Hello All,

I am a time series neophyte, so please be gentle.

I am working on a project where the data are a series of events that states send amongst each other over time.
DV (events that one state sends to another state) = f(domestic factors, & other events that are being sent around the system)

The first approach that I used was to model this with OLS, adding lagged values of the DV (and one of the IVs) until the errors from the OLS were indistinguishable from white noise. This seemed fine. The problem that I found was that there is evidence of ARCH effects when I ran post regression diagnostic tests.

I am not interested in modeling the volatility over time. I am interested in obtaining the correct estimates for the IVs that are of theoretical interest. Further, I have no theoretical reason to believe in a certain sort of risk-aversion or acceptance, so the broader GARCH family of estimators does not seem (to me anyways) to be really relevant.

So far, I have tried the archlm command, which I interpreted as a LM test to establish the order of the p process in the GARCH(p,q) model. After consulting Enders (1995), I also used the squared errors from the regression (p. 147-8) and calculated the Ljung-Box Q stat, which corroborated the problem with conditional heteroskedascity (corrgram on the squared errors). The problem that I have is how to determine what the order of the q process, and how this may affect the order of the p process.

Now, there may be one large problem with the data itself. It is about 6300 observations of daily data, where linear interpolation was used to fill the gaps (average gap length < 4 days in the DV, the gap varies across the IVs) in the events data (days where the actors did not send events) so that the number of observations would be reasonable for analysis. I know that this introduces massive autocorrelation in the data, and therefore I used lagged variables in the OLS, but I did not think that this would systematically affect the ARCH-like process.

The model converges with a (1,1) (2,1) (1,2) and (2,2) GARCH specification. The coefficients for p 1-2 and q 1 are significant in the (2,2), but I am not certain if that is really a useful criterion.

I read the archive of this listserv, and the earlier posting about optimal GARCH length warned about over-parameterization and comparing the ML of the different models, but I wondered if anyone could share some additional information or ideas about how to find the correct GARCH specification in Stata.

Thanks for your time,

Chad

--
Dr. Chad Atkinson
Department of Political Science
314 Millett Hall
Wright State University
3640 Colonel Glenn Hwy.
Dayton, OH 45419-0001

937.775.2903
chad.atkinson@wright.edu

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