Bootstrap inference in cointegrated VAR models

Abstract

The main problem discussed in this work may be described as the lack of coherence between the test statistics and their reference distribution. In small sample the approximations of the first order asymptotic theory are often quite inaccurate. As a result the empirical and nominal probabilities that a test rejects a correct hypothesis can be very different when critical values based on first-order approximation are used. This may lead one to reject too many null hypotheses when they are actually true. In principle there are two ways of solving this problem; either for a given reference distribution to correct the test statistic or for a given test statistic to correct the reference distribution. In Chapter 2 of this thesis we consider Johansen's likelihood ratio and Wald tests for linear restrictions on cointegrating space and we compare analytical corrections to the test statistics such as the ones suggested by Podivinsky and Psaradakis with a numerical approximation of the distribution function obtained using computer intensive methods such as the bootstrap. In Chapter 3 we approximate the finite sample expectation of the likelihood ratio test using the bootstrap and we compare the finite sample properties of the asymptotic, the bootstrap, and the bootstrap Bartlett corrected likelihood ratio tests. Furthermore, we propose bootstrapping the Bartlett corrected likelihood ratio test, using the Bartlett correction proposed by Johansen (1999). In Chapter 4 we provide an empirical application to illustrate the usefulness of the bootstrap test using real data in place of the simulated ones.

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