[R-SIG-Finance] ljung-box tests in arma and garch models

[Dale Rosenthal]

I think Patrick is technically correct; but, the point may be
moot for many analyses.  Here's why:

The Box and Ljung-Box statistics are asymptotically
chi-squared.  For iid normal rhos (autocorrelation
coefficients), that is exact.

However, if the rhos are correlated (not unusual) or few in
number (for tests of smaller models), large-scale asymptotics
may offer poor approximations.

For correlated rhos (say corr(rho_j, rho_k) is about 0.2),
large-scale approximations will probably be fine for tests of
3 or more lags.  But higher correlations will decrease the
accuracy of small-model tests.

I discuss similar small-sample approximations in a working
paper: (Data Delays, Index Deletions, Prepayments, and
Defaults,
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1032671). 
Keep in mind that the chi-squared is a special case of the gamma.

Dale

>Message: 3
>Date: Sun, 30 Dec 2007 18:54:23 +0000
>From: "John Frain" <frainj at tcd.ie>
>Subject: Re: [R-SIG-Finance] ljung-box tests in arma and
garch models
>
>For a proof that the appropriate degrees of freedom is
>s-p-q see Brockwell and Davis (1990), Time Series: Theory
>and Methods, 2nd Edition, Springer, page 310.
>
>John Frain
>
>[...]