Time Series – ARIMA Modeling for White Noise Probabilities vs. Residual Autocorrelation and PACF

arimaforecastingresidualstime serieswhite noise

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.
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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.

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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.

Best Answer

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.

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