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st: error variance increases when we add a variable in a GARCH model


From   "John Levendis" <johnlevendis@business.loyno.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: error variance increases when we add a variable in a GARCH model
Date   Wed, 30 Jan 2013 10:01:29 -0600

Dear Statalisters,

I'm stuck and I need the benefit of your wisdom.

I'm trying to estimate a GARCH(1,1) model, with and without an exogenous
variable. My dependent variable is usually some financial stock's daily
returns. Sometimes, when I add the exogenous variable to the model, the
error variance actually increases; i.e. the model fits *worse* when I
include an extra variable. I was under the impression that
goodness-of-fit never goes down when you add a variable. Any ideas why
I'm getting this strange result? Is it just because the models are
estimated iteratively, and the likelihood isn't quite maxed out?

My Stata code is below.

Thanks in advance.

--John

************************************************************************
*****************
set more off
fetchyahooquotes UTX SPY, freq(d) chg(ln) start(01jan2000) /* Downloads
daily data on stock UTX and the S&P*/

gen day=_n 
tsset day 

arch ln_UTX L(1/2).ln_UTX, arch(1) garch(1) nolog
predict double resid_restricted, resid 

arch ln_UTX L(1/2).ln_UTX L(1/2).ln_SPY, arch(1) garch(1) nolog
predict double resid_unrestricted, resid 

sum resid*
************************************************************************
*****************

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