A Simple Nonparametric Long-Run Correlation Estimator

A simple consistent nonparametric estimator of the long-run correlation between two series is proposed, based on the estimation of the bivariate k-lag difference correlation. It is shown that the estimator is asymptotically equivalent to the Bartlett kernel spectral estimator of the complex coherency at frequency zero. The asymptotic distribution is derived, with a test for the absence of long-run correlation. An optimal lag-selection criterion is also presented. Monte Carlo experiments are used to evaluate the proposed estimator. I am grateful to F. Araújo, S. Durlauf, J. Faria, B. Hansen, M. Horvath, Y. Kitamura, B. Tabak and particularly K. West for many helpful comments and suggestions. I am nevertheless solely responsible for remaining errors.