Nonparametric cointegration analysis

provided by Research Papers in Economics

Nonparametric Cointegration Analysis

Herman J. Bierens¹

Southern Methodist University, Dallas, Texas, U.S.A.,
and

Tilburg University, the Netherlands

In this paper we propose consistent cointegration tests, and estimators of a basis of the space
of cointegrating vectors, that do not need specification of the data-generating process, apart
from some mild regularity conditions, or estimation of structural and/or nuisance parameters.
This nonparametric approach is in the same spirit as Johansen’s LR method in that the test
statistics involved are obtained from the solutions of a generalized eigenvalue problem, and
the hypotheses to be tested are the same, but in our case the two matrices in the generalized
eigenvalue problem involved are constructed independently of the data-generating process. We
compare our approach empirically as well as by a limited Monte Carlo simulation with
Johansen’s approach, using the series for ln(wages) and ln(GNP) from the extended Nelson-
Plosser data.

Key words: Cointegration, unit roots, nonparametric, nuisance parameter free, hypotheses
testing, estimation

JEL Codes: C12, C14, C32

First draft: November 1993. First revision: September 1994. Second revision:
September 1, 1995

¹ Correspondence address: Department of Economics, Southern Methodist University,
Dallas, Texas 75275, U.S.A.; e-mail: [email protected], phone: (+1)-214-7683856, fax:
(+1)-214-7681821. This paper was written and revised while enjoying the hospitality of Tilburg
University during the summers of 1993, 1994 and 1995. The helpful comments of Manfred
Deistler, Philip Hans Franses, Noud van Giersbergen, Esfandiar Maasoumi, Rolf Tschernig, Ben
Vogelvang, and four referees, are gratefully acknowledged. Previous versions of this paper have
been presented at the University of Amsterdam, Free University of Amsterdam, University of
Houston-Rice University, Texas A&M University, Tinbergen Institute Rotterdam, the University
of British Columbia, the University of Virginia, ESEM 1994, and the ERNSI Econometric
Workshop 1995, the Netherlands.

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