In the development of forecasting, prediction or estimation models, we have recourse to information criterions so that the model is parsimonious. So, why and when should one or the other of these information criterions be used ?
When you want to compare non-nested models.
But I wonder why you mention forcast, prediction and estimation. IC's value the observed data realtive to the given model. This is does not (or only to a very tiny amount) allow to judge how the model performs in forcast, prediction and estimation.
You may wish to look at the attached papers and their references for examples and discussion. Questions are welcomed. Best wishes, David Booth
You need to be mindful of what any one IC is doing for you. They can look at 3 different contexts:
(a) you select a model structure now, fit the model to the data you have now and keep using those now-fitted parameters from now on.
(b) you select a model structure now and keep that structure, but will refit the model to an expanded dataset (reducing parameter-estimation variation but not bias).
(c) you select a model structure now and keep that structure, but will continually refit the model as expanded datasets are available (eliminating parameter-estimation variation but not bias).
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