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Moderate deviations for quadratic forms in Gaussian stationary processes


  • Kakizawa, Yoshihide


Moderate deviations limit theorem is proved for quadratic forms in zero-mean Gaussian stationary processes. Two particular cases are the cumulative periodogram and the kernel spectral density estimator. We also derive the exponential decay of moderate deviation probabilities of goodness-of-fit tests for the spectral density and then discuss intermediate asymptotic efficiencies of tests.

Suggested Citation

  • Kakizawa, Yoshihide, 2007. "Moderate deviations for quadratic forms in Gaussian stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 992-1017, May.
  • Handle: RePEc:eee:jmvana:v:98:y:2007:i:5:p:992-1017

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    References listed on IDEAS

    1. Bercu, B. & Gamboa, F. & Rouault, A., 1997. "Large deviations for quadratic forms of stationary Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 71(1), pages 75-90, October.
    2. Velasco, Carlos & Robinson, Peter M., 2001. "Edgeworth Expansions For Spectral Density Estimates And Studentized Sample Mean," Econometric Theory, Cambridge University Press, vol. 17(03), pages 497-539, June.
    3. Taniguchi, Masanobu & van Garderen, Kees Jan & Puri, Madan L., 2003. "Higher Order Asymptotic Theory For Minimum Contrast Estimators Of Spectral Parameters Of Stationary Processes," Econometric Theory, Cambridge University Press, vol. 19(06), pages 984-1007, December.
    4. Yoshihide Kakizawa, 2006. "Bernstein polynomial estimation of a spectral density," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(2), pages 253-287, March.
    5. Daniel Janas, 1994. "Edgeworth expansions for spectral mean estimates with applications to Whittle estimates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(4), pages 667-682, December.
    6. Zani, Marguerite, 2002. "Large Deviations for Quadratic Forms of Locally Stationary Processes," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 205-228, May.
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