Exact Local Whittle Estimation of Fractionally Cointegrated Systems

Abstract

Semiparametric estimation of a bivariate fractionally cointegrated system is considered. The new estimator employs the exact local Whittle approach developed by Shimotsu and Phillips (2003a) and estimates the two memory parameters jointly with the cointegrating vector. It permits both (asymptotically) stationary and nonstationary stochastic trends and/or equilibrium errors without relying on differencing or data tapering. Indeed, the asymptotic properties of the estimator depend only on the difference of the two memory parameters. The estimator of the memory parameters is shown to be consistent and asymptotically normally distributed in both stationary and nonstationary cases.