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

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  • Kim, Byungsoo
  • Lee, Sangyeol

Abstract

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.

Suggested Citation

  • Kim, Byungsoo & Lee, Sangyeol, 2013. "Robust estimation for the covariance matrix of multivariate time series based on normal mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 125-140.
    • 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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    References listed on IDEAS

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    1. Salvatore Ingrassia, 2004. "A likelihood-based constrained algorithm for multivariate normal mixture models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 13(2), pages 151-166, September.
    2. 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.
    3. Isabelle Huault & V. Perret & S. Charreire-Petit, 2007. "Management," Post-Print halshs-00337676, HAL.
    4. 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.
    5. 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.
    6. Yanyuan Ma & Marc G. Genton, 2000. "Highly Robust Estimation of the Autocovariance Function," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(6), pages 663-684, November.
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    Cited by:

    1. Kim, Byungsoo, 2018. "Robust maximum entropy test for GARCH models based on a minimum density power divergence estimator," Economics Letters, Elsevier, vol. 162(C), pages 93-97.
    2. Song, Junmo & Oh, Dong-hyun & Kang, Jiwon, 2017. "Robust estimation in stochastic frontier models," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 243-267.
    3. Byungsoo Kim & Sangyeol Lee, 2014. "Minimum density power divergence estimator for covariance matrix based on skew $$t$$ t distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(4), pages 565-575, November.
    4. Byungsoo Kim & Sangyeol Lee, 2020. "Robust estimation for general integer-valued time series models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(6), pages 1371-1396, December.

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