Co-Integration Rank Testing under Conditional Heteroskedasticity

CREATES Research Paper No. 2009-22

48 Pages Posted: 28 May 2009

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

Date Written: May 28, 2009

Abstract

We analyse the properties of the conventional Gaussian-based co-integrating rank tests of Johansen (1996) in the case where the vector of series under test is driven by globally stationary, conditionally heteroskedastic (martingale difference) innovations. We first demonstrate that the limiting null distributions of the rank statistics coincide with those derived by previous authors who assume either i.i.d. or (strict and covariance) stationary martingale difference innovations. We then propose wild bootstrap implementations of the co-integrating rank tests and demonstrate that the associated bootstrap rank statistics replicate the first-order asymptotic null distributions of the rank statistics. We show the same is also true of the corresponding rank tests based on the i.i.d. bootstrap of Swensen (2006). The wild bootstrap, however, has the important property that, unlike the i.i.d. bootstrap, it preserves in the re-sampled data the pattern of heteroskedasticity present in the original shocks. Consistent with this, numerical evidence suggests that, relative to tests based on the asymptotic critical values or the i.i.d. bootstrap, the wild bootstrap rank tests perform very well in small samples under a variety of conditionally heteroskedastic innovation processes. An empirical application to the term structure of interest rates is given.

Keywords: Co-integration, trace and maximum eigenvalue rank tests, conditional heteroskedasticity, i.i.d. bootstrap, wild bootstrap

JEL Classification: C30, C32

Suggested Citation

Cavaliere, Giuseppe and Rahbek, Anders and Taylor, A. M. Robert, Co-Integration Rank Testing under Conditional Heteroskedasticity (May 28, 2009). CREATES Research Paper No. 2009-22, Available at SSRN: https://ssrn.com/abstract=1411046 or http://dx.doi.org/10.2139/ssrn.1411046

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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