The problem is that, with exogenous variables in the variance equation, the
asymptotic standard deviation of the residuals depends, in general, on the
stationary marginal distribution of the exogenous variables. However, if the
exogenous variables are deterministic function that are used, for example,
to account for outliers or level shifts in variance, then the formula for
the asymptotic variance can be easily modified.
You can always try to compute the unconditional variance yourself. For
example, for the GARCH(1,1) with variance equation
Sigma(t)^2 = w + alpha*e(t-1)^2 + beta*sigma(t-1)^2
the unconditional variance is simply
w/(1 - alpha - beta)
With a stationary exogenous variable x(t), the variance equation becomes
Sigma(t)^2 = w + delta*x(t-1) + alpha*e(t-1)^2 + beta*sigma(t-1)^2
And the unconditional variance is
(w + delta*E[x])/(1 - alpha - beta)
Hope this helps. ez
-----Original Message-----
From: s-news-owner@lists.biostat.wustl.edu
[mailto:s-news-owner@lists.biostat.wustl.edu] On Behalf Of Abhijit Sarkar
Sent: Friday, August 04, 2006 4:15 PM
To: s-news@lists.biostat.wustl.edu
Subject: [S] problem in deriving unconditional std dev (asymp.sd) in garch
Hi!
Why does the
>estimated.eqn$asymp.sd
command for deriving unconditional std dev of GARCH residuals returns
1[NA] whenever exogeneous explanatory variables are included in the
conditional variance equation?
eg. command including exogeneous explanatory variables in conditional
variance equation, returning an NA:
>private.egarch<-garch(private~1, x=ytmfin, z=sigma.ytmfin,
+ series.start=2, x.start=2, z.start=2, ~egarch(1,1),leverage=T)
>usd=private.egarch$asymp.sd
>usd
[1]NA
but once you drop z (ie. the exogoneous explanatory variable in
conditional volatility equation), the problem disappears:
>private.egarch.noZ<-garch(private~1, x=ytmfin,
+ series.start=2, x.start=2, ~egarch(1,1),leverage=T)
> usd.noZ = private.egarch.noZ$asymp.sd
> usd.noZ
[1] 0.0374903
I was basically trying to estimate the news impact curve. The above
problem persists with tgarch and pgarch also (...and garch too).
--
Abhijit Sarkar
UGC-SRF (Economics)
Dept. of Humanities and Social Sciences
IIT Bombay
Powai, Mumbai,
Maharashtra, India, 400076
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