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When using fable to produce a set of different ARIMA models using different combinations of xregs, if different models choose a different d and D parameters then the AICc are no longer comparable, right? In that case, should I just find the max d and D chosen from all the models and fix those parameters and retrain the models for comparison?

Tyler Smith
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  • could you clarify about "different combinations of x regs?" – Miguel Trejo Aug 04 '20 at 13:14
  • @MiguelTrejo Different combinations, as in, one model specification might be `y ~ x1` and another `y ~ x2` and a third is `y ~ x1 + x2`. So in my scenario, `y` and `x1` may be stationary, but `x2` is not. – Tyler Smith Aug 04 '20 at 15:59

2 Answers2

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Correct, information criterions can only be compared when the model uses the same response variable (same transformation, same differencing).

The automatic selection algorithm uses the regression residuals to perform repeated unit root tests to identify the appropriate d and D parameters. If you're varying the exogenous regressors, the choice of d and D may vary.

To compare the models via AICc you will need to keep the differencing fixed. Alternatively, you can compare ARIMA models with different amounts of differencing using other accuracy measures via the accuracy() function (more details here: https://otexts.com/fpp3/accuracy.html)

Mitchell O'Hara-Wild
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@Mitchel, if you have the following models:

  • y ~ ARIMA
  • y ~ ARIMA + xreg_1
  • y ~ ARIMA + xreg_2
  • y ~ ARIMA + xreg_1 + xreg_2,

Can you compare the AICs between these models directly? can you select the best model to forecast y from these four different models just minimising the AICc?

BqKaXeu29y
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  • As it’s currently written, your answer is unclear. Please [edit] to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers [in the help center](/help/how-to-answer). – Community Jan 21 '23 at 04:19
  • If these ARIMA models have the same level of differencing, yes. – Mitchell O'Hara-Wild Jan 25 '23 at 00:22