Uniform inference in autoregressive models

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.