Diebold Chapter 5 : Model Selection (Consistency)

[thirtywinks]

Hi all,

I'm having trouble understanding the conditions for a model selection criterion to demonstrate consistency. Can anyone help to provide an example of how this can be applied with the criterions (S^2, AIC, SIC) and how the true model comes into the picture?

Thanks a lot!

 

[ShaktiRathore]

Hi,
consistency condition is a property which satisfies the following:As sample size increases when the model selection criterion is applied to a collection of models which also contain the true model then the true model shall be selected by the criterion consistently. SIC criterion being the most conservative applying the most penalty on the MSE therefore its most likely that the true model shall gets selected therefore SIC satisfies consistency property,if true model is there then SIC shall select that model .AIC and S^2 can select models other than true model also due to less penalty applied to MSE therefore SIC is more consistent in selecting only the true model. SIC satisfies the consistency property the most. Whenever SIC is applied to a group of models the true model if present is consistently selected and rejecting other models.
thanks