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. enter image description here enter image description here

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.

enter image description here enter image description here

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.

1 Answer 1


Acf and pacf is usually sufficient. The suggestion about lag 4 structure might mean an omItted monthly effect. Try adding 11 deterministic monthly dummies to your model since your Intervention Diagnostic tool may mot have this important diagnostic capability. For grins you might try downloading other automatic software and see how it is treated there.

  • $\begingroup$ Great Thanks. Do you think specifying a lag 4 is more parsimonious than using 11 dummies? if I had use lag 4, how would I write this using the following notation (4,1,0)(0,1,1)52? $\endgroup$
    – forecaster
    Jul 21, 2015 at 18:05
  • $\begingroup$ It all depends on how many of the 11 dummies are significant' as the insignificant ones should be discarded. $\endgroup$
    – IrishStat
    Jul 21, 2015 at 18:51
  • $\begingroup$ the answer to your question "how would I write.." is you can't use the pdq notation to represent that as you wish to constrain lags 1,2,3 to be absent.and therefore you can't use any software that limits you to pdq notation . AUTOBOX or SAS could be used as they have much more generality of expression. $\endgroup$
    – IrishStat
    Jul 22, 2015 at 8:03

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