I have moderate understanding of statistics and time series analysis. I trying to forecast a weekly time series with lots of outliers and trend shifts. After correcting all of the outliers, I'm left with the following residual panel. The final model is (0,1,0)X(0,1,1)52 + Outlier Correction.
In looking at the acf/pacf I see no pattern. However when I look at the white noise probabilities, I see that there is significant autocorrelation left at lag 4. so I modify the above model to (4,1,0)X(0,1,1)52+Outlier Correction. Please note that it is not AR(4) but instead AR(0,0,0,1) model. I get the diagnostic plots as shown below. I no longer have any significant autocorrelation left in white noise probablities.
Below are my questions:
- Do we really need to be concerned about white noise probabilities or is it suffice to look in to ACF and PACF of residuals and ensure that there is no pattern left?.
- Does the white noise probabilities matter if the goal is prediction/forecast ? There is not much difference between the forecasted values in two models.