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Confidence estimation of the covariance function of stationary and locally stationary processes

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  • Giurcanu Mihai
  • Spokoiny Vladimir

Abstract

In this note we consider the problem of confidence estimation of the covariance function of a stationary or locally stationary zero mean Gaussian process. The constructed confidence intervals are based on the usual empirical covariance estimate and a special estimate of its variance. The results about coverage probability are stated in a nonasymptotic way and apply for small and moderate sample size under mild conditions on the model. The presented numerical results are in agreement with the theoretical issues and demonstrate applicability of the method.

Suggested Citation

  • Giurcanu Mihai & Spokoiny Vladimir, 2004. "Confidence estimation of the covariance function of stationary and locally stationary processes," Statistics & Risk Modeling, De Gruyter, vol. 22(4), pages 283-300, April.
    • Handle: RePEc:bpj:strimo:v:22:y:2004:i:4/2004:p:283-300:n:3
    DOI: 10.1524/stnd.22.4.283.64315
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    References listed on IDEAS

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    1. Hernando Ombao & Jonathan Raz & Rainer von Sachs & Wensheng Guo, 2002. "The SLEX Model of a Non-Stationary Random Process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(1), pages 171-200, March.
    2. Spokoiny, Vladimir, 2002. "Variance Estimation for High-Dimensional Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 111-133, July.
    3. Dahlhaus, R., 1996. "On the Kullback-Leibler information divergence of locally stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 139-168, March.
    4. Sakiyama, Kenji & Taniguchi, Masanobu, 2004. "Discriminant analysis for locally stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 90(2), pages 282-300, August.
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