Estimating Fractional Cointegration in the Presence of Polynomial Trends

Abstract

We propose and derive the asymptotic distribution of a tapered narrow-band least squares estimator (NBLSE) of the cointegration parameter β in the framework of fractional cointegration. This tapered estimator is invariant to deterministic polynomial trends. In particular, we allow for arbitrary linear time trends that often occur in practice. Our simulations show that, in the case of no deterministic trends, the estimator is superior to ordinary least squares (OLS) and the nontapered NBLSE proposed by P.M. Robinson when the levels have a unit root and the cointegrating relationship between the series is weak. In terms of rate of convergence, our estimator converges faster under certain circumstances, and never slower, than either OLS or the nontapered NBLSE. In a data analysis of interest rates, we find stronger evidence of cointegration if the tapered NBLSE is used for the cointegration parameter than if OLS is used.