A1 Refereed original research article in a scientific journal
Statistical properties of a blind source separation estimator for stationary time series
Authors: Miettinen J, Nordhausen K, Oja H, Taskinen S
Publisher: ELSEVIER SCIENCE BV
Publication year: 2012
Journal: Statistics and Probability Letters
Journal name in source: STATISTICS & PROBABILITY LETTERS
Journal acronym: STAT PROBABIL LETT
Volume: 82
Issue: 11
First page : 1865
Last page: 1873
Number of pages: 9
ISSN: 0167-7152
DOI: https://doi.org/10.1016/j.spl.2012.06.025
Abstract
In this paper, we assume that the observed p time series are linear combinations of p latent uncorrelated weakly stationary time series. The problem is then, using the observed p-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(infinity) processes. (C) 2012 Elsevier B.V. All rights reserved.
In this paper, we assume that the observed p time series are linear combinations of p latent uncorrelated weakly stationary time series. The problem is then, using the observed p-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(infinity) processes. (C) 2012 Elsevier B.V. All rights reserved.
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