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

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  • Miettinen, Jari
  • Nordhausen, Klaus
  • Oja, Hannu
  • Taskinen, Sara

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(∞) processes.

Suggested Citation

  • Miettinen, Jari & Nordhausen, Klaus & Oja, Hannu & Taskinen, Sara, 2012. "Statistical properties of a blind source separation estimator for stationary time series," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1865-1873.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:11:p:1865-1873
    DOI: 10.1016/j.spl.2012.06.025
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    References listed on IDEAS

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    1. Ilmonen, Pauliina & Nevalainen, Jaakko & Oja, Hannu, 2010. "Characteristics of multivariate distributions and the invariant coordinate system," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1844-1853, December.
    2. Su, Nan & Lund, Robert, 2012. "Multivariate versions of Bartlett’s formula," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 18-31.
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    Cited by:

    1. Lietzén, Niko & Nordhausen, Klaus & Ilmonen, Pauliina, 2016. "Minimum distance index for complex valued ICA," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 100-106.
    2. Jari Miettinen & Markus Matilainen & Klaus Nordhausen & Sara Taskinen, 2020. "Extracting Conditionally Heteroskedastic Components using Independent Component Analysis," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 293-311, March.
    3. Taskinen, Sara & Miettinen, Jari & Nordhausen, Klaus, 2016. "A more efficient second order blind identification method for separation of uncorrelated stationary time series," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 21-26.
    4. François Bachoc & Marc G Genton & Klaus Nordhausen & Anne Ruiz-Gazen & Joni Virta, 2020. "Spatial blind source separation," Biometrika, Biometrika Trust, vol. 107(3), pages 627-646.
    5. Jari Miettinen & Katrin Illner & Klaus Nordhausen & Hannu Oja & Sara Taskinen & Fabian J. Theis, 2016. "Separation of Uncorrelated Stationary time series using Autocovariance Matrices," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 337-354, May.
    6. Nordhausen, Klaus & Ruiz-Gazen, Anne, 2022. "On the usage of joint diagonalization in multivariate statistics," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    7. Matilainen, Markus & Nordhausen, Klaus & Oja, Hannu, 2015. "New independent component analysis tools for time series," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 80-87.
    8. Matilainen, M. & Croux, C. & Nordhausen, K. & Oja, H., 2017. "Supervised dimension reduction for multivariate time series," Econometrics and Statistics, Elsevier, vol. 4(C), pages 57-69.
    9. Miettinen, Jari & Nordhausen, Klaus & Oja, Hannu & Taskinen, Sara, 2014. "Deflation-based separation of uncorrelated stationary time series," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 214-227.

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