Estimating Fractional Cointegration in the Presence of Polynomial Trends
27 Pages Posted: 31 Oct 2008
Date Written: February 2003
We propose and derive the asymptotic distribution of a tapered narrow-band least squares estimator(NBLSE) of the cointegration parameter ÃÂÃÂ² in the framework of fractional cointegration.This tapered estimator is invariant to deterministic polynomial trends. In particular, we allowfor arbitrary linear time trends that often occur in practice. Our simulations show that, in thecase of no deterministic trends, the estimator is superior to ordinary least squares (OLS) and thenontapered NBLSE proposed by P.M. Robinson when the levels have a unit root and the cointegratingrelationship between the series is weak. In terms of rate of convergence, our estimatorconverges faster under certain circumstances, and never slower, than either OLS or the nontaperedNBLSE. In a data analysis of interest rates, we find stronger evidence of cointegration ifthe tapered NBLSE is used for the cointegration parameter than if OLS is used.
Keywords: Fractional cointegration, Long memory, Tapering, Periodogram
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