Department of Economics and Business Economics

Bootstrap Sequential Determination of the Co-integration Rank in VAR Models

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  • Cavaliere Guiseppe, University of Bologna, Italy
  • Anders Rahbæk, Denmark
  • A.M. Robert Taylor, University of Nottingham, United Kingdom
  • School of Economics and Management
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
of Johansen (1996) can be unreliable in small samples with empirical rejection
frequencies 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 Carlo
simulations show the proposed procedure performs well in practice.
Original languageEnglish
Place of publicationAarhus
PublisherInstitut for Økonomi, Aarhus Universitet
Number of pages23
Publication statusPublished - 2010

    Research areas

  • Co-integration, trace test, sequential rank determination, i.i.d.bootstrap, wild bootstrap

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