Local Whittle Analysis of Stationary Fractional Cointegration

We consider a local Whittle analysis of a stationary fractionally cointegrated model. A two step estimator equivalent to the local Whittle QMLE is proposed to jointly estimate the integration orders of the regressors, the integration order of the errors, and the cointegration vector. The estimator is semiparametric in the sense that it employs local assumptions on the joint spectral density matrix of the regressors and the errors near the zero frequency. We show that, for the entire stationary region of the integration orders, the estimator is asymptotically normal with block diagonal covariance matrix. Thus, the estimates of the integration orders are asymptotically independent of the estimate of the cointegration vector. Furthermore, our estimator of the cointegrating vector is asymptotically normal for a wider range of integration orders than the narrow band frequency domain least squares estimator and is superior with respect to asymptotic variance. An application to financial volatility series is offered.