I needed to find an adequate model for a time series using SAS and I found two slightly different models that were adequate according to the white noise test. All of the transformations and things I added to the model were also significant according to SAS but there are still about 4 lags that are slightly sticking out for the auto correlations and partial auto correlations. The four lags that are sticking out are spread out between lags 30 and 100, the entire data has 397 lags, and it's the same lags that are slightly sticking out for both the auto correlations and partial auto correlations. Is it possible that a model can be adequate but still have a few lags that slightly stick out?
If your sample size is large ( and I guess it is if you have lags 397 ) then the std .error of the ACF is going to be very small ( 1/sqrt(nob) ) thus you are probably getting a false rejection. If you want you can post the SAS output , the model , the data and your residuals and I might be able to comment/help further.