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The maximum of the periodogram

Author

Listed:
  • An, Hong-Zhi
  • Chen, Zhao-Guo
  • Hannan, E. J.

Abstract

Let x(t), t = 1,..., T, be generated by a zero mean stationary process and let I([omega]) = [Sigma]x(t)expit[omega]2/T be the periodogram. Under general conditions, and in particular assuming only a finite 2nd moment, it is shown that max[omega]I([omega])/{2[pi]f([omega])logT}

Suggested Citation

  • An, Hong-Zhi & Chen, Zhao-Guo & Hannan, E. J., 1983. "The maximum of the periodogram," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 383-400, September.
    • Handle: RePEc:eee:jmvana:v:13:y:1983:i:3:p:383-400
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    Citations

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    Cited by:

    1. Hassler, U. & Marmol, F. & Velasco, C., 2006. "Residual log-periodogram inference for long-run relationships," Journal of Econometrics, Elsevier, vol. 130(1), pages 165-207, January.
    2. Song, Kai-Sheng & Li, Ta-Hsin, 2000. "A statistically and computationally efficient method for frequency estimation," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 29-47, March.
    3. Hidalgo, Javier & Zaffaroni, Paolo, 2007. "A goodness-of-fit test for ARCH([infinity]) models," Journal of Econometrics, Elsevier, vol. 141(2), pages 973-1013, December.
    4. A. M. Walker, 2003. "A note on estimation by least squares for harmonic component models," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(5), pages 613-629, September.
    5. Hidalgo, Javier, 2009. "Goodness of fit for lattice processes," Journal of Econometrics, Elsevier, vol. 151(2), pages 113-128, August.
    6. Lazarova, Stepana, 2005. "Testing for structural change in regression with long memory processes," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 329-372.
    7. Carlos Velasco & Ignacio N. Lobato, 2004. "A simple and general test for white noise," Econometric Society 2004 Latin American Meetings 112, Econometric Society.
    8. Kokoszka, Piotr & Mikosch, Thomas, 2000. "The periodogram at the Fourier frequencies," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 49-79, March.
    9. Hidalgo, Javier, 2003. "An alternative bootstrap to moving blocks for time series regression models," Journal of Econometrics, Elsevier, vol. 117(2), pages 369-399, December.
    10. Hidalgo, Javier, 2003. "A bootstrap causality test for covariance stationary processes," LSE Research Online Documents on Economics 6848, London School of Economics and Political Science, LSE Library.
    11. Hidalgo, J., 2005. "A bootstrap causality test for covariance stationary processes," Journal of Econometrics, Elsevier, vol. 126(1), pages 115-143, May.
    12. Javier Hidalgo, 2003. "A Bootstrap Causality Test for Covariance Stationary Processes," STICERD - Econometrics Paper Series 462, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    13. Javier Hidalgo & Philippe Soulier, 2004. "Estimation of the location and exponent of the spectral singularity of a long memory process," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(1), pages 55-81, January.

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