Supplementary Appendix to "Uniform Inference in Autoregressive Models"

The Supplementary Appendix contains proofs of some results stated in the paper "Uniform Inference in Autoregressive Models" by Anna Mikusheva. In particular, it provides a proof of a statement about strong approximation, proofs of Lemmas 11 and 12 from the paper about the asymptotic approximations for scheme of series. It also proves results stated in Remarks 2, 3 and 4 for AR(1) processes with a linear time trend. Section 5 proves the validity of parametric and non-parametric grid bootstrap procedures for AR(p) processes with at most one root close to the unit circle. Section 7 contains an extensive Monte-Carlo study of finite sample properties of discussed methods. We keep notations introduced in the paper.

Supplemental Authors: 
Anna Mikusheva