Low-pass filtered least squares estimators of cointegrating vectors

This paper proposes a class of low-pass filtered least squares estimators of cointegrating vectors. It is shown that (1) the filtered least squares estimators may reduce the second order bias; (2) while the filtered fully modified least squares estimators share the same asymptotic efficiency as the fully modified least squares estimators, the filtered fully modified least squares may gain efficiency in finite samples; and (3) the filtered fully modified Wald tests have asymptotic χ2 distributions. A Monte Carlo study indicates that the finite sample properties are consistent with the asymptotic results, and, in particular, the filtering method for removing high-frequency components significantly improves OLS and FMLS cointegrating estimators, with the gains from filtering being significant in finite samples.