I am performing the Box-Pierce Q Statistic  test and wonder Where to get the Critical 10% level of the chi square values please?

[NEAS: Use Excel or R; or Google "chi-square"]

wdu

What do you use to get the Box Pierce Q statistic?

I have seen in the book that

Q = T*sum(r^2) where r = sum(e(t)*e(t-k))/sum(e(t)^2)

So how do we get e(t-k) when we should use k = 100? Do we start at e(101) and multiply that by the first residual e(1), sum all those up.

I am quite confused on this part and it is the last part of the project that I need to complete to describe my model.

[NEAS: Yes. The numerator has fewer terms than the denominator, which adjusts for degrees of freedom in the correlations.]

So if you have K=100 and a total of 10 years of data points (T= 3652). Would you use the above mentioned formula to get your Q statistic, and compare this to a chi-squared critical value of 10% and 3652 data points - the number of parameters (1 for AR(1) etc)?

If i am basing my AR models off of one years worth of points (T = 365) should i instead use K as 100 and T as 365 and only calculate the Q statistic based on the residuals from the 365 points?

Thanks for the help