A1 Refereed original research article in a scientific journal
Deflation-based separation of uncorrelated stationary time series
Authors: Miettinen J, Nordhausen K, Oja H, Taskinen S
Publisher: ELSEVIER INC
Publication year: 2014
Journal: Journal of Multivariate Analysis
Journal name in source: JOURNAL OF MULTIVARIATE ANALYSIS
Journal acronym: J MULTIVARIATE ANAL
Volume: 123
First page : 214
Last page: 227
Number of pages: 14
ISSN: 0047-259X
DOI: https://doi.org/10.1016/j.jmva.2013.09.009(external)
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 to find an estimate for an unmixing matrix that transforms the observed time series back to uncorrelated time series. The so called SOBI (Second Order Blind Identification) estimate aims at a joint diagonalization of the covariance matrix and several autocovariance matrices with varying lags. In this paper, we propose a novel procedure that extracts the latent time series one by one. The limiting distribution of this deflation-based SOBI is found under general conditions, and we show how the results can be used for the comparison of estimates. The exact formula for the limiting covariance matrix of the deflation-based SOBI estimate is given for general multivariate MA(infinity) processes. Finally, a whole family of estimates is proposed with the deflation-based SOBI as a special case, and the limiting properties of these estimates are found as well. The theory is widely illustrated by simulation studies. (C) 2013 Elsevier Inc. 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 to find an estimate for an unmixing matrix that transforms the observed time series back to uncorrelated time series. The so called SOBI (Second Order Blind Identification) estimate aims at a joint diagonalization of the covariance matrix and several autocovariance matrices with varying lags. In this paper, we propose a novel procedure that extracts the latent time series one by one. The limiting distribution of this deflation-based SOBI is found under general conditions, and we show how the results can be used for the comparison of estimates. The exact formula for the limiting covariance matrix of the deflation-based SOBI estimate is given for general multivariate MA(infinity) processes. Finally, a whole family of estimates is proposed with the deflation-based SOBI as a special case, and the limiting properties of these estimates are found as well. The theory is widely illustrated by simulation studies. (C) 2013 Elsevier Inc. All rights reserved.
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