st: Determining correct lag structure for GARCH model

[Chad Atkinson <chad.atkinson@wright.edu>]

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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