Root-N-Consistent Estimation of Weak Fractional Cointegration

43 Pages Posted: 21 Jul 2008

Date Written: March 2006


Empirical evidence has emerged of the possibility of fractional cointegration such that the gap, β, between the integration order δ of observable time series, and the integration order γ of cointegrating errors, is less than 0.5. This includes circumstances when observables are stationary or asymptotically stationary with long memory (so δ < 1/2), and when they are nonstationary (so δ 1/2). This "weak cointegration" contrasts strongly with the traditional econometric prescription of unit root observables and short memory cointegrating errors, where β = 1. Asymptotic inferential theory also differs from this case, and from other members of the class β > 1/2, in particular ≥ consistent - n and asymptotically normal estimation of the cointegrating vector ν is possible when β < 1/2, as we explore in a simple bivariate model. The estimate depends on γ and δ or, more realistically, on estimates of unknown γ and δ. These latter estimates need to be consistent - n , and the asymptotic distribution of the estimate of ν is sensitive to their precise form. We propose estimates of γ and δ that are computationally relatively convenient, relying on only univariate nonlinear optimization. Finite sample performance of the methods is examined by means of Monte Carlo simulations, and several applications to empirical data included.

JEL Classification: C32

Suggested Citation

Hualde, Javier, Root-N-Consistent Estimation of Weak Fractional Cointegration (March 2006). LSE STICERD Research Paper No. EM499, Available at SSRN:

Javier Hualde (Contact Author)

University of Navarra ( email )

Pamplona, Navarra 31080