Inference for Stationary Processes Using Banded Covariance Matrices

  • Mohsen Pourahmadi
  • Wei Biao Wu
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

We consider prediction and estimation problems by banding covariance matrices of stationary processes. Under a novel short-range dependence condition for a class of nonlinear processes, it is shown that the banded covariance matrix estimates converge in operator norm to the true covariance matrix with reasonable rates of convergence. A sub-sampling approach is proposed to choose the banding parameter.


Time Series Data Covariance Matrice Toeplitz Matrice Nonlinear Time Series Covariance Matrix Estimate 
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  1. [1]
    Bickel, P. J. and Levina, E.: Regularized estimation of large covariance matrices. (2006).∼bickel/techrep.pdf
  2. [2]
    Bryc, W., Dembo, A. and and Jiang, T.: Spectral measure of large random Hankel, Markov and Toeplitz matrices. Ann. Probab. 34, 138 (2006).CrossRefMathSciNetGoogle Scholar
  3. [3]
    El Karoui, N.: Tracy-Widom limit for the largest eigenvalue of a large class of com-plex sample covariance matrices. Ann. Probab. 35, 663-714 (2007).MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Hannan, E.J. and Deistler, M.: The Statistical Theory of Linear Systems. Wiley, New York. (1988).MATHGoogle Scholar
  5. [5]
    Johnstone, I.M.: On the distribution of the largest eigenvalue in principal compo-nents analysis. Ann. Statist. 29, 295-327 (2001).MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Politis, D.N., Roman, J.P. and Wolf, M.: Subsampling. Springer Series in Statistics, New York. (1999).MATHGoogle Scholar
  7. [7]
    Pourahmadi, M.: Foundations of Time Series Analysis and Prediction Theory. Wiley, New York. (2001).MATHGoogle Scholar
  8. [8]
    Tong, H.: Non-linear Time Series: A Dynamical System Approach. Oxford Scienti c Publications. (1990).Google Scholar
  9. [9]
    Wu, W. B.: Nonlinear system theory: Another look at dependence. Proceedings of the National Academy of Sciences USA. 102, 14150-14154 (2005).MATHCrossRefGoogle Scholar
  10. [10]
    Wu, W.B. and X. Shao: Limit Theorems for Iterated Random Functions. Journal of Applied Probability. 41, 425-436 (2004).MATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    Zeitouni, O. and Anderson, G.W.: A CLT for regularized sample covariance matrices. Ann. of Statist. To appear. (2008).Google Scholar

Copyright information

© Physica-Verlag Heidelberg 2008

Authors and Affiliations

  • Mohsen Pourahmadi
    • 1
  • Wei Biao Wu
    • 2
  1. 1.Northern Illinois UniversityUSA
  2. 2.University of ChicagoUSA

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