Comparing AICc of ARIMA models produced in fable
Question
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?
2 answers
solution1
0 2020-09-23 02:45:38
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 )
solution2
0 2023-01-20 23:02:05
@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?
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