Cointegration in Fractional Systems with Unkown Integration Orders

49 Pages Posted: 21 Jul 2008

Date Written: February 2003


The semiparametric local Whittle or Gaussian estimate of the long memory parameter is known to have especially nice limiting distributional properties, being asymptotically normal with a limiting variance that is completely known. However in moderate samples the normal approximation may not be very good, so we consider a refined, Edgeworth, approximation, for both a tapered estimate, and the original untapered one. For the tapered estimate, our higher-order correction involves two terms, one of order 1/√m (where m is the bandwidth number in the estimation), the other a bias term, which increases in m; depending on the relative magnitude of the terms, one or the other may dominate, or they may balance. For the untapered estimate we obtain an expansion in which, for m increasing fast enough, the correction consists only of a bias term. We discuss applications of our expansions to improved statistical inference and bandwidth choice. We assume Gaussianity, but in other respects our assumptions seem mild.

JEL Classification: C13, C14

Suggested Citation

Hualde, Javier, Cointegration in Fractional Systems with Unkown Integration Orders (February 2003). LSE STICERD Research Paper No. EM449, Available at SSRN:

Javier Hualde (Contact Author)

University of Navarra ( email )

Pamplona, Navarra 31080