Accurate and (almost) tuning parameter free inference in cointegrating regressions

Abstract

Tuning parameter choices complicate statistical inference in cointegrating regressions and affect finite sample distributions of test statistics. As commonly used asymptotic theory fails to capture these effects, tests often suffer from severe size distortions. We propose a novel self-normalized test statistic for general linear hypotheses, which avoids the choice of tuning parameters. Its limiting null distributions is nonstandard, but simulating asymptotically valid critical values is straightforward. To further improve the performance of the test in small to medium samples, we employ the vector autoregressive sieve bootstrap to construct critical values. To show its consistency, we establish a bootstrap invariance principle result under conditions that go beyond the assumptions commonly imposed in the literature. Simulation results demonstrate that our new test outperforms competing approaches, as it has good power properties and is considerably less prone to size distortions.