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Robust estimation for the covariance matrix of multivariate time series based on normal mixtures

Listed author(s):
  • Kim, Byungsoo
  • Lee, Sangyeol
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    In this paper, we study the robust estimation for the covariance matrix of stationary multivariate time series. As a robust estimator, we propose to use a minimum density power divergence estimator (MDPDE) designed by Basu et al. (1998). To supplement the result of Kim and Lee (2011), we employ a multivariate normal mixture family instead of a multivariate normal family. As a special case, we consider the robust estimator for the autocovariance function of univariate stationary time series. It is shown that the MDPDE is strongly consistent and asymptotically normal under regularity conditions. Simulation results are provided for illustration. A real data analysis applied to the portfolio selection problem is also considered.

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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 57 (2013)
    Issue (Month): 1 ()
    Pages: 125-140

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    Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:125-140
    DOI: 10.1016/j.csda.2012.06.012
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    1. B. Clarke & C. Heathcote, 1994. "Robust estimation ofk-component univariate normal mixtures," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(1), pages 83-93, March.
    2. Isabelle Huault & V. Perret & S. Charreire-Petit, 2007. "Management," Post-Print halshs-00337676, HAL.
    3. Keewhan Choi, 1969. "Estimators for the parameters of a finite mixture of distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 107-116, December.
    4. Byungsoo Kim & Sangyeol Lee, 2011. "Robust estimation for the covariance matrix of multi‐variate time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(5), pages 469-481, September.
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