Inference on Co-Integration Parameters in Heteroskedastic Vector Autoregressions

52 Pages Posted: 28 Nov 2013

See all articles by H. Peter Boswijk

H. Peter Boswijk

Amsterdam School of Economics; Tinbergen Institute

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 - Essex Business School; University of Essex

Multiple version iconThere are 2 versions of this paper

Date Written: November 14, 2013

Abstract

It is well established that the shocks driving many key macro-economic and financial variables display time-varying volatility. In this paper we consider estimation and hypothesis testing on the coefficients of the co-integrating relations and the adjustment coefficients in vector autoregressions driven by both conditional and unconditional heteroskedasticity of a quite general and unknown form in the shocks. We show that the conventional results in Johansen (1996) for the maximum likelihood estimators and associated likelihood ratio tests derived under homoskedasticity do not in general hold in the presence of heteroskedasticity. As a consequence, standard confidence intervals and tests of hypothesis on these coefficients are potentially unreliable. Solutions to this inference problem based on Wald tests (using a "sandwich" estimator of the variance matrix) and on the use of the wild bootstrap are discussed. These do not require the practitioner to specify a parametric model for volatility, or to assume that the pattern of volatility is common to, or independent across, the vector of series under analysis. We formally establish the conditions under which these methods are asymptotically valid. A Monte Carlo simulation study demonstrates that significant improvements in finite sample size can be obtained by the bootstrap over the corresponding asymptotic tests in both heteroskedastic and homoskedastic environments. An application to the term structure of interest rates in the US illustrates the difference between standard and bootstrap inferences regarding hypotheses on the co-integrating vectors and adjustment coefficients.

Keywords: Co-integration, adjustment coefficients, (un)conditional heteroskedasticity, heteroskedasticity-robust inference, wild bootstrap

JEL Classification: C30, C32

Suggested Citation

Boswijk, H. Peter and Cavaliere, Giuseppe and Rahbek, Anders and Taylor, A. M. Robert, Inference on Co-Integration Parameters in Heteroskedastic Vector Autoregressions (November 14, 2013). Univ. of Copenhagen Dept. of Economics Discussion Paper No. 13-13, Available at SSRN: https://ssrn.com/abstract=2359441 or http://dx.doi.org/10.2139/ssrn.2359441

H. Peter Boswijk (Contact Author)

Amsterdam School of Economics ( email )

Roetersstraat 11
Amsterdam, North Holland 1018 WB
Netherlands

HOME PAGE: http://www.uva.nl/profile/h.p.boswijk

Tinbergen Institute ( email )

Burg. Oudlaan 50
Rotterdam, 3062 PA
Netherlands

Giuseppe Cavaliere

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

Ă˜ster Farimagsgade 5
Bygning 26
1353 Copenhagen K.
Denmark

A. M. Robert Taylor

University of Essex - Essex Business School ( email )

Wivenhoe Park
Colchester, CO4 3SQ
United Kingdom

University of Essex ( email )

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