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Second-order expansion for the maximum of some stationary Gaussian sequences

Author

Listed:
  • Barbe, Ph.
  • McCormick, W. P.

Abstract

We prove a second-order approximation formula for the distribution of the largest term among an infinite moving average Gaussian sequence. The second-order correction term depends on the autocovariance function only through the second largest autocovariance. Applications to Gaussian time series are discussed and a simulation study showed a substantial improvement over other approximations to the exact distribution of the maximum.

Suggested Citation

  • Barbe, Ph. & McCormick, W. P., 2004. "Second-order expansion for the maximum of some stationary Gaussian sequences," Stochastic Processes and their Applications, Elsevier, vol. 110(2), pages 315-342, April.
    • Handle: RePEc:eee:spapps:v:110:y:2004:i:2:p:315-342
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    References listed on IDEAS

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    1. Mittal, Y. & Ylvisaker, D., 1975. "Limit distributions for the maxima of stationary Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 3(1), pages 1-18, January.
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