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Nonparametric Cointegration Analysis of Fractional Systems with Unknown Integration Orders

CREATES Research Paper 2009-2

39 Pages Posted: 15 Jan 2009  

Morten Ørregaard Nielsen

Queen's University - Department of Economics

Date Written: January 12, 2009


In this paper a nonparametric variance ratio testing approach is proposed for determining the number of cointegrating relations 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. 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.

Keywords: Cointegration rank, cointegration space, fractional integration and cointegration, interest rates, long memory, nonparametric, term structure, variance ratio

JEL Classification: C32

Suggested Citation

Nielsen, Morten Ørregaard, Nonparametric Cointegration Analysis of Fractional Systems with Unknown Integration Orders (January 12, 2009). CREATES Research Paper 2009-2. Available at SSRN: or

Morten Orregaard Nielsen (Contact Author)

Queen's University - Department of Economics ( email )

94 University Avenue
Kingston K7L 3N6, Ontario


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