Statistical properties of a blind source separation estimator for stationary time series

In this paper, we assume that the observed pp time series are linear combinations of pp latent uncorrelated weakly stationary time series. The problem is then, using the observed pp-variate time series, to find an estimate for a mixing or unmixing matrix for the combinations. The estimated uncorrelated time series may then have nice interpretations and can be used in a further analysis. The popular AMUSE algorithm finds an estimate of an unmixing matrix using covariances and autocovariances of the observed time series. In this paper, we derive the limiting distribution of the AMUSE estimator under general conditions, and show how the results can be used for the comparison of estimates. The exact formula for the limiting covariance matrix of the AMUSE estimate is given for general MA(∞)(∞) processes.