there are two estimated competing models AR(i) and AR(j) (i != j). Does BIC(i)<AIC(j) suggest we should choose AR(i) model?
Note: T is sufficiently large.


这是我自己的答案，但我觉得有些问题
Yes. Because that the BIC estimator of the lag length, i, in an autoregression is correct in lagrge samples (Recall that T is sufficiently large). That is, Pr(i=p)→1. This is not true for the AIC estimator, which can overestimate p even in large samples.