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Deflation-based separation of uncorrelated stationary time series

Author

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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 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(∞) 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.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:123:y:2014:i:c:p:214-227
    DOI: 10.1016/j.jmva.2013.09.009
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    References listed on IDEAS

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    1. Su, Nan & Lund, Robert, 2012. "Multivariate versions of Bartlett’s formula," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 18-31.
    2. 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.
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    Cited by:

    1. 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.
    2. Klaus Nordhausen & Anne Ruiz-Gazen, 2022. "On the usage of joint diagonalization in multivariate statistics," Post-Print hal-04296111, HAL.
    3. 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.
    4. Nordhausen, Klaus & Ruiz-Gazen, Anne, 2021. "On the usage of joint diagonalization in multivariate statistics," TSE Working Papers 21-1268, Toulouse School of Economics (TSE).
    5. 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.
    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. Bachoc, François & Genton, Mark G. & Nordhausen, Klaus & Ruiz-Gazen, Anne & Virta, Joni, 2019. "Spatial Blind Source Separation," TSE Working Papers 19-998, Toulouse School of Economics (TSE).
    8. 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.

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