[R-SIG-Finance] P values in coefficients from garch fitting

[Eric Zivot]

In S-PLUS the default p-values used by summary.mgarch() are based on the
Student's t distribution. Here is the relevant code where the p-value is
computed

pv <- 2 * (1 - pt(abs(tv), xdf))

and pt() is the function for computing the cdf of the Student's t
distribution with xdf degrees of freedom. 

What is important is not the p-value distribution but the formula for the
asymptotic variance of the garch estimates. In splus the default is to use
the inverse of the numerical Hessian of the garch likelihood. Typically this
is the Gaussian distribution. However, S-plus has the option of computing
the Quasi maximum likelihood asymptotic variance based on the so-called
sandwich formula. 

In my experience garch estimates vary considerably across software packages
(see the review articles by Chris Brooks for more details). This is mainly
due to different optimizers, different convergence parameters etc. As a
result, one would not expect the p-values (or estimates) to match exactly
across different software. 


-----Original Message-----
From: r-sig-finance-bounces at stat.math.ethz.ch
[mailto:r-sig-finance-bounces at stat.math.ethz.ch] On Behalf Of ShyhWeir Tzang
Sent: Sunday, November 11, 2007 3:41 PM
To: r-sig-finance at stat.math.ethz.ch
Subject: [R-SIG-Finance] P values in coefficients from garch fitting

Dear all:

I have seen different p values of the estimated coefficients using R and
S-plus after running the garch-fitting procedures. Why? Eviews denote that
the p values are z values. What are the distribution used in R and S-Plus?
Thanks for  your help.

ShyhWeir Tzang

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