I have fit an auto-regressive model to a data series. The model seems to explain the given data relatively well given that the total $R^2$ is 0.95. However, SAS has a diagnostic plot called white noise test in proc autoreg. Past lag 10, the null hypothesis of white noise is rejected in this plot. i.e the bands go past the 0.05 level. (this seems bad) The acf and pacf plots for the residuals seem to be fine as all bars are inside the error bands. (this is as expected)
I'm wondering if anyone can explain the impact that a white noise test like this will have on my model.
Particularly, I am interested in how valid it makes the $R^2$ value. I am only interested in explaining my current data – not in prediction. As such, I am mostly just interested in the validity of the $R^2$ value.
Due to privacy considerations, I cannot post my diagnostic plots, but they are essentially the same as the figure in this question : ARIMA modeling white noise probabilities vs. residual autocorrelation/PACF
Best Answer
If the data set is seasonal say monthly it is possible that if this is left untreated in your model one could get rejection beyond lag 10. In general the bands around a sample acf/pacf are VERY APPROXIMATE and should be looked at with skepticism as they are based upon a VERY APPROXIMATE standard error prewsumption.