Nonparametric cointegration analysis of fractional systems with unknown integration orders

TY - JOUR

T1 - Nonparametric cointegration analysis of fractional systems with unknown integration orders

AU - Nielsen, Morten Ørregaard

N1 - Funding Information: The author is grateful to the editor, Peter Robinson, two anonymous referees, an anonymous associate editor, Søren Johansen, Marius Ooms, and Tim Vogelsang for their comments and suggestions that significantly improved the paper. He also thank the seminar participants at Cornell University, Purdue University, Queen’s University, and University of Wisconsin–Madison as well as the participants at TSEFAR 2006, the Econometrics in Rio 2006 Conference, the European Meeting of the Econometric Society 2006, and the CREATES Symposium on Long Memory 2007 for their comments and discussion, and the Social Sciences and Humanities Research Council of Canada (SSHRC grant no. 410-2009-0183), the Danish Social Sciences Research Council (FSE grant no. 275-05-0220), the Center for Analytic Economics (CAE) at Cornell University, and the Center for Research in Econometric Analysis of Time Series (CREATES, funded by the Danish National Research Foundation) at the University of Aarhus for research support.

PY - 2010/4

Y1 - 2010/4

N2 - In this paper a nonparametric variance ratio testing approach is proposed for determining the cointegration rank in fractionally integrated systems. The test statistic is easily calculated without prior knowledge of the integration order of the data, the strength of the cointegrating relations, or the cointegration vector(s). The latter property makes it easier to implement than regression-based approaches, especially when examining relationships between several variables with possibly multiple cointegrating vectors. Since the test is nonparametric, it does not require the specification of a particular model and is invariant to short-run dynamics. Nor does it require the choice of any smoothing parameters that change the test statistic without being reflected in the asymptotic distribution. Furthermore, a consistent estimator of the cointegration space can be obtained from the procedure. The asymptotic distribution theory for the proposed test is non-standard but easily tabulated or simulated. Monte Carlo simulations demonstrate excellent finite sample properties, even rivaling those of well-specified parametric tests. The proposed methodology is applied to the term structure of interest rates, where, contrary to both fractional- and integer-based parametric approaches, evidence in favor of the expectations hypothesis is found using the nonparametric approach.

AB - In this paper a nonparametric variance ratio testing approach is proposed for determining the cointegration rank in fractionally integrated systems. The test statistic is easily calculated without prior knowledge of the integration order of the data, the strength of the cointegrating relations, or the cointegration vector(s). The latter property makes it easier to implement than regression-based approaches, especially when examining relationships between several variables with possibly multiple cointegrating vectors. Since the test is nonparametric, it does not require the specification of a particular model and is invariant to short-run dynamics. Nor does it require the choice of any smoothing parameters that change the test statistic without being reflected in the asymptotic distribution. Furthermore, a consistent estimator of the cointegration space can be obtained from the procedure. The asymptotic distribution theory for the proposed test is non-standard but easily tabulated or simulated. Monte Carlo simulations demonstrate excellent finite sample properties, even rivaling those of well-specified parametric tests. The proposed methodology is applied to the term structure of interest rates, where, contrary to both fractional- and integer-based parametric approaches, evidence in favor of the expectations hypothesis is found using the nonparametric approach.

KW - Cointegration rank

KW - Cointegration space

KW - Fractional integration and cointegration

KW - Interest rates

KW - Long memory

KW - Nonparametric

KW - Term structure

KW - Variance ratio

UR - http://www.scopus.com/inward/record.url?scp=77649270329&partnerID=8YFLogxK

U2 - 10.1016/j.jeconom.2009.10.002

DO - 10.1016/j.jeconom.2009.10.002

M3 - Journal article

AN - SCOPUS:77649270329

SN - 0304-4076

VL - 155

SP - 170

EP - 187

JO - Journal of Econometrics

JF - Journal of Econometrics

IS - 2

ER -