Should I be trying to replicate the NEAS results?

[NEAS: This is an independent student project. The NEAS postings are suggestions to get you started. You can construct an ARIMA model, compare two or more models for a given era, compare two or three eras by type of model of by model parameters, examine seasonality, test out-of-sample forecasts, and many other items.]

I just have a few questions regarding applying the Box-Pierce Q statistic.

I have 52 data points on which i fit a variety of ARIMA models.

To test if the residuals of the model form a white noise, i use the Q statistic:

When i take 1st and 2nd differences i'm essentially left with fewer data points.

So do i still use T=52, or do i use T=50 for the 2nd differenced Time Series?

[NEAS: T = 50]

Also, the Q statistic has (K-p-q) degrees of freedom.

But if i fit an AR(2) model with an annual lag term for seasonality (making the model AR(12)), then what is the value of p?

Is it 12 or 2 or 3?

[NEAS: 3]