On asymptotic risk of selecting models for possibly nonstationary time-series

Abstract

To prove Lemmas 1-3, we need the following five auxiliary lemmas: Lemmas B.1-B.5.Lemma B.1. Suppose the assumptions in Theorem 1 hold. For k 0 ≤ k ≤ k(n), and all q ≥ 2, max k 0 ≤k≤k(n)