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

37 Pages Posted: 5 Sep 2012

See all articles by Giuseppe Cavaliere

Giuseppe Cavaliere

University of Bologna

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: August 1, 2012

Abstract

In a recent paper Cavaliere et al. (2012) develop bootstrap implementations of the (pseudo-) likelihood ratio [PLR] co-integration rank test and associated sequential rank determination procedure of Johansen (1996). The bootstrap samples are constructed using the restricted parameter estimates of the underlying VAR model which obtain under the reduced rank null hypothesis. They propose methods based on an i.i.d. bootstrap re-sampling scheme and establish the validity of their proposed bootstrap procedures in the context of a co-integrated VAR model with i.i.d. innovations.

In this paper we investigate the properties of their bootstrap procedures, together with analogous procedures based on a wild bootstrap re-sampling scheme, when time-varying behaviour is present in either the conditional or unconditional variance of the innovations. We show that the bootstrap PLR tests are asymptotically correctly sized and, moreover, that the probability that the associated bootstrap sequential procedures select a rank smaller than the true rank converges to zero. This result is shown to hold for both the i.i.d. and wild bootstrap variants under conditional heteroskedasticity but only for the latter under unconditional heteroskedasticity. Monte Carlo evidence is reported which suggests that the bootstrap approach of Cavaliere et al. (2012) significantly improves upon the nite sample performance of corresponding procedures based on either the asymptotic PLR test or an alternative bootstrap method (where the short run dynamics in the VAR model are estimated unrestrictedly) for a variety of conditionally and unconditionally heteroskedastic innovation processes.

Keywords: Bootstrap, Co-integration, Trace statistic, Rank determination, heteroskedasticity

JEL Classification: C30, C32

Suggested Citation

Cavaliere, Giuseppe and Rahbek, Anders and Taylor, A. M. Robert, Bootstrap Determination of the Co-Integration Rank in Heteroskedastic VAR Models (August 1, 2012). Univ. of Copenhagen Dept. of Economics Discussion Paper No. 12-11. Available at SSRN: https://ssrn.com/abstract=2141220 or http://dx.doi.org/10.2139/ssrn.2141220

Giuseppe Cavaliere

University of Bologna ( email )

Via Belle Arti 41
Bologna, 40125
Italy
+39 0512098230 (Phone)
+39 051232153 (Fax)

Anders Rahbek (Contact Author)

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 Nottingham - School of Economics ( email )

University Park
Nottingham, NG7 2RD
United Kingdom

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