Dynamic OLS estimation of fractionally cointegrated regressions

In this paper we study estimation and inference of cointegration vector(s) in a fractionally cointegrated system employing a regression-based approach. In "strongly cointegrated" regressions (when the difference between integration order of observables and cointegration errors exceeds 1/2) the OLS estimator of the cointegration vector does not have an optimal rate of convergence in a part of parameter space. We use the approach of Saikkonen (1991) appending the regression equation with leads and lags of filtered regressor and estimate cointegration vector with OLS in the appended regression in this way obtaining optimal convergence rate and local asymptotic mixed normal distribution of the estimator. Although the estimator depends on the values of integration order and cointegration strength, we show that use of consistent estimates does not affect asymptotic properties of the estimator. This allows to construct feasible Wald test for
linear restrictions on the coefficients with nuisance-free asymptotic null distribution. Monte
Carlo study illustrating finite sample properties of the estimator and Wald test is provided.