Accurate and (almost) tuning parameter free inference in cointegrating regressions
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Date
2020
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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.
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Keywords
bootstrap invariance principle, vector autoregressive sieve bootstrap, self-normalization, inference, IM-OLS, cointegration