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Moderate deviations for quadratic forms in Gaussian stationary processes

  • Kakizawa, Yoshihide
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    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.

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    File URL: http://www.sciencedirect.com/science/article/B6WK9-4M04DW1-1/2/2c5356f12e24e0ccd87d56103876f71e
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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 98 (2007)
    Issue (Month): 5 (May)
    Pages: 992-1017

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    Handle: RePEc:eee:jmvana:v:98:y:2007:i:5:p:992-1017
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    1. 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.
    2. 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.
    3. 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.
    4. Yoshihide Kakizawa, 2006. "Bernstein polynomial estimation of a spectral density," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(2), pages 253-287, 03.
    5. Daniel Janas, 1994. "Edgeworth expansions for spectral mean estimates with applications to Whittle estimates," Annals of the Institute of Statistical Mathematics, Springer, 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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