Local Covariance Estimation using Costationarity

In this paper we propose a novel estimator for the time-varying covariance of locally stationary time series. This new approach is based upon costationary combinations of such time series, that is, time-varying deterministic combinations returning stationary processes. We show with a simulation example that the new estimator has smaller variance than the available competitors which are exclusively based on the evolutionary cross-periodogram, and can therefore be appealing in a large number of applications.