Testing for Co-Integration in Vector Autoregressions with Non-Stationary Volatility

39 Pages Posted: 3 Oct 2008

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

Robert Taylor

University of Essex; University of Essex - Essex Business School

Date Written: September 8, 2008

Abstract

Many key macro-economic and financial variables are characterised by permanent changes in unconditional volatility. In this paper we analyse vector autoregressions with non-stationary (unconditional) volatility of a very general form, which includes single and multiple volatility breaks as special cases. We show that the conventional rank statistics computed as in Johansen (1988,1991) are potentially unreliable. In particular, their large sample distributions depend on the integrated covariation of the underlying multivariate volatility process which impacts on both the size and power of the associated co-integration tests, as we demonstrate numerically. A solution to the identified inference problem is provided by considering wild bootstrap-based implementations of the rank tests. These do not require the practitioner to specify a parametric model for volatility, nor to assume that the pattern of volatility is common to, or independent across, the vector of series under analysis. The bootstrap is shown to perform very well in practice.

Keywords: Co-integration, non-stationary volatility, trace and maximum eigenvalue tests, wild bootstrap

JEL Classification: C30, C32

Suggested Citation

Cavaliere, Giuseppe and Rahbek, Anders and Taylor, A. M. Robert and Taylor, A. M. Robert, Testing for Co-Integration in Vector Autoregressions with Non-Stationary Volatility (September 8, 2008). CREATES Research Paper No. 2008-50, Univ. of Copenhagen Dept. of Economics Discussion Paper No. 08-34, Available at SSRN: https://ssrn.com/abstract=1264907 or http://dx.doi.org/10.2139/ssrn.1264907

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 Essex ( email )

University of Essex - Essex Business School ( email )

Wivenhoe Park
Colchester, CO4 3SQ
United Kingdom

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