Estimating Fractional Cointegration in the Presence of Polynomial Trends

We propose and derive the asymptotic distribution of a tapered narrow-band least squaresestimator (NBLSE) of the cointegration parameter Icirc;² in the framework of fractional cointegration. Thistapered estimator is invariant to deterministic polynomial trends. In particular, we allow for arbitrarylinear time trends that often occur in practice. Our simulations show that, in the case of no deterministictrends, the estimator is superior to ordinary least squares (OLS) and the nontapered NBLSE proposedby P.M. Robinson when the levels have a unit root and the cointegrating relationship between the seriesis weak. In terms of rate of convergence, our estimator converges faster under certain circumstances, andnever slower, than either OLS or the nontapered NBLSE. In a data analysis of interest rates, we findstronger evidence of cointegration if the tapered NBLSE is used for the cointegration parameter than ifOLS is used