No, the df are H-(p+q), against what your intuition tells you. The problem is that you're thinking of the residuals as losing a df for each parameter, but the asymptotics of the problem involve the sample autocorrelations of the residuals. You can read the details in the original paper by Box and Pierce (?Box.test for the reference). By the way, you're not alone, Minitab makes the same mistake you did.
> David Stoffer wrote:
>> >> I stand corrected. I thought I checked this a long time ago, but >> apparently not. tsdiag.Arima DOES NOT use the fact that the series it is >> testing (or diagnosing, if you will) are residuals from an ARIMA fit. >> >> I keep a list of R time series bloopers here: >> http://www.stat.pitt.edu/stoffer/tsa2/Rissues.htm along with some >> work-arounds over here: >> http://www.stat.pitt.edu/stoffer/tsa2/Examples.htm >> >>
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