Separation of Uncorrelated Stationary time series using Autocovariance Matrices

In blind source separation, one assumes that the observed p time series are linear combinations of p latent uncorrelated weakly stationary time series. To estimate the unmixing matrix, which transforms the observed time series back to uncorrelated latent time series, second-order blind identification (SOBI) uses joint diagonalization of the covariance matrix and autocovariance matrices with several lags. In this article, we find the limiting distribution of the well-known symmetric SOBI estimator under general conditions and compare its asymptotical efficiencies to those of the recently introduced deflation-based SOBI estimator. The theory is illustrated by some finite-sample simulation studies.