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Optimal correction of an indefinite estimated MA spectral density matrix

Author

Listed:
  • Stoica, Petre
  • Xu, Luzhou
  • Li, Jian
  • Xie, Yao

Abstract

Consider a vector moving-average sequence of order n, MA(n), and let denote its spectral density matrix, where are the covariance matrices and [omega] stands for the frequency variable. A nonparametric estimate of [Phi]([omega]) can easily become indefinite at some frequencies, and thus invalid, due to the estimation errors. In this paper, we provide a computationally efficient procedure that obtains the optimal (in a least-squares sense) valid approximation [Phi]([omega]) to in a polynomial time, by means of a semidefinite programming (SDP) algorithm.

Suggested Citation

  • Stoica, Petre & Xu, Luzhou & Li, Jian & Xie, Yao, 2007. "Optimal correction of an indefinite estimated MA spectral density matrix," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 973-980, June.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:10:p:973-980
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    References listed on IDEAS

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    1. Li, Lei M., 2005. "Factorization of moving-average spectral densities by state-space representations and stacking," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 425-438, October.
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