I chose a project which interested me, instead of a template project, and I think I bit off more than I can chew.

I developed an ARIMA model based on 114 records, with 117 observations each, and I am trying to run the Box Pierce Test.  For T, should I use 117 (observations per record) or 13,338 (114 * 117 total observations)?

Using 13,338 produces a Box Pierce statistic for the entire group which is significantly greater than for any one idividual.  This would cause me to reject the null hypothesis (that the residuals follow a white noise process) at the 1% significance level for the entire group, but not reject it at a 50% significance level for 71 of the 114 individual members.  I would think that the model would work much better on the group as a whole than on any individual record (unless I got VERY lucky in choosing the record).