Bootstrap Sequential Determination of the Co-Integration Rank in VAR Models
CREATES Research Paper No. 2010-7
25 Pages Posted: 11 Feb 2010
There are 2 versions of this paper
Bootstrap Sequential Determination of the Co-Integration Rank in VAR Models
Date Written: February 10, 2010
Abstract
Determining the co-integrating rank of a system of variables has become a fundamental aspect of applied research in macroeconomics and finance. It is wellknown that standard asymptotic likelihood ratio tests for co-integration rank f Johansen (1996) can be unreliable in small samples with empirical rejectionfrequencies often very much in excess of the nominal level. As a consequence, bootstrap versions of these tests have been developed. To be useful, however, sequential procedures for determining the co-integrating rank based on these bootstrap tests need to be consistent, in the sense that the probability of selecting a rank smaller than (equal to) the true co-integrating rank will converge to zero (one minus the marginal significance level), as the sample size diverges, for general I(1) processes. No such likelihood-based procedure is currently known to be available. In this paper we fill this gap in the literature by proposing a bootstrap sequential algorithm which we demonstrate delivers consistent cointegration rank estimation for general I(1) processes. Finite sample Monte Carlosimulations show the proposed procedure performs well in practice.
Keywords: Co-integration, trace test, sequential rank determination, i.i.d.bootstrap, wild bootstrap
JEL Classification: C30, C32
Suggested Citation: Suggested Citation