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Discrete and continuous expectation formulae for level-crossings, upcrossings and excursions of ellipsoidal processes

Author

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  • Tanaka, Minoru
  • Shimizu, Kunio

Abstract

The paper provides the expected level-crossing count, the expected level-crossing rate, the expected number of upcrossings and the expected length of excursions above a fixed level in a strictly stationary ellipsoidal process whose finite dimensional distributions are scale mixtures of normal distributions.

Suggested Citation

  • Tanaka, Minoru & Shimizu, Kunio, 2001. "Discrete and continuous expectation formulae for level-crossings, upcrossings and excursions of ellipsoidal processes," Statistics & Probability Letters, Elsevier, vol. 52(3), pages 225-232, April.
    • Handle: RePEc:eee:stapro:v:52:y:2001:i:3:p:225-232
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    Cited by:

    1. Shimizu, Kunio & Tanaka, Minoru, 2003. "Expected number of level-crossings for a strictly stationary ellipsoidal process," Statistics & Probability Letters, Elsevier, vol. 64(3), pages 305-310, September.
    2. Alexeev, Vitali & Maynard, Alex, 2012. "Localized level crossing random walk test robust to the presence of structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3322-3344.
    3. Yuichi Goto & Masanobu Taniguchi, 2020. "Discriminant analysis based on binary time series," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(5), pages 569-595, July.

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