I would like to thank Graham Elliott, Bruce Hansen, Rustam Ibragimov, and Allie Schwartz for comments and suggestions. Suggestions from four anonymous referees and a co-editor greatly improved the paper. I am grateful to Marcelo Moreira for numerous discussions, his enthusiasm, and his support. I am deeply indebted to Jim Stock for posing the question, and for his help, support, and encouragement. I would like to thank Aleksander Bulinski for introducing me to the theory of stochastic processes and Skorokhod's embedding. I thank Donald Andrews and Patrik Guggenberger for finding some technical difficulties in an earlier version of the paper. All remaining errors are mine.
Uniform Inference in Autoregressive Models
Article first published online: 3 AUG 2007
Volume 75, Issue 5, pages 1411–1452, September 2007
How to Cite
Mikusheva, A. (2007), Uniform Inference in Autoregressive Models. Econometrica, 75: 1411–1452. doi: 10.1111/j.1468-0262.2007.00798.x
- Issue published online: 3 AUG 2007
- Article first published online: 3 AUG 2007
- Manuscript received January, 2006; final revision received February, 2007.
Vol. 78, Issue 5, 1773, Article first published online: 12 OCT 2010
- Autoregressive process;
- confidence set;
- local-to-unity asymptotics;
- uniform convergence
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.