Econometrica: Sep 2007, Volume 75, Issue 5

Uniform Inference in Autoregressive Models

DOI: 10.1111/j.1468-0262.2007.00798.x
p. 1411-1452

Anna Mikusheva

The purpose of this paper is to provide theoretical justification for some existing methods for constructing confidence intervals for the sum of coefficients in autoregressive models. We show that the methods of Stock (1991), Andrews (1993), and Hansen (1999) provide asymptotically valid confidence intervals, whereas the subsampling method of Romano and Wolf (2001) does not. In addition, we generalize the three valid methods to a larger class of statistics. We also clarify the difference between uniform and pointwise asymptotic approximations, and show that a pointwise convergence of coverage probabilities for all values of the parameter does not guarantee the validity of the confidence set.

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Supplemental Material

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.

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