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

24 Pages Posted: 12 Feb 2010

See all articles by Giuseppe Cavaliere

Giuseppe Cavaliere

University of Bologna - Department of Economics

Anders Rahbek

University of Copenhagen - Department of Statistics and Operations Research; University of Copenhagen - Department of Economics

A. M. Robert Taylor

University of Nottingham - School of Economics

Multiple version iconThere are 2 versions of this paper

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 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.

Keywords: co-integration, trace test, sequential rank determination, i.i.d. bootstrap, wild bootstrap

JEL Classification: C30, C32

Suggested Citation

Cavaliere, Giuseppe and Rahbek, Anders and Taylor, A. M. Robert, Bootstrap Sequential Determination of the Co-Integration Rank in VAR Models (February 10, 2010). Univ. of Copenhagen Dept. of Economics Discussion Paper No. 10-07, Available at SSRN: https://ssrn.com/abstract=1551822 or http://dx.doi.org/10.2139/ssrn.1551822

Giuseppe Cavaliere (Contact Author)

University of Bologna - Department of Economics ( email )

Bologna
Italy
+390512098489 (Phone)

Anders Rahbek

University of Copenhagen - Department of Statistics and Operations Research

Universitetsparken 5
DK-2100
Denmark
+45 3532 0682 (Phone)

University of Copenhagen - Department of Economics

Øster Farimagsgade 5
Bygning 26
1353 Copenhagen K.
Denmark

A. M. Robert Taylor

University of Nottingham - School of Economics ( email )

University Park
Nottingham, NG7 2RD
United Kingdom

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