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Asymptotic theory for curve-crossing analysis

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  • Zhao, Zhibiao
  • Wu, Wei Biao

Abstract

We consider asymptotic properties of curve-crossing counts of linear processes and nonlinear time series by curves. Central limit theorems are obtained for curve-crossing counts of short-range dependent processes. For the long-range dependence case, the asymptotic distributions are shown to be either multiple Wiener-Itô integrals or integrals with respect to stable Lévy processes, depending on the heaviness of tails of the underlying processes.

Suggested Citation

  • Zhao, Zhibiao & Wu, Wei Biao, 2007. "Asymptotic theory for curve-crossing analysis," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 862-877, July.
  • Handle: RePEc:eee:spapps:v:117:y:2007:i:7:p:862-877
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    References listed on IDEAS

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    1. Romano, Joseph P. & Wolf, Michael, 2000. "A more general central limit theorem for m-dependent random variables with unbounded m," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 115-124, April.
    2. Kratz, Marie F. & León, JoséR., 1997. "Hermite polynomial expansion for non-smooth functionals of stationary Gaussian processes: Crossings and extremes," Stochastic Processes and their Applications, Elsevier, vol. 66(2), pages 237-252, March.
    3. Giraitis, Liudas & Koul, Hira L. & Surgailis, Donatas, 1996. "Asymptotic normality of regression estimators with long memory errors," Statistics & Probability Letters, Elsevier, vol. 29(4), pages 317-335, September.
    4. Biao Wu, Wei & Min, Wanli, 2005. "On linear processes with dependent innovations," Stochastic Processes and their Applications, Elsevier, vol. 115(6), pages 939-958, June.
    5. 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.
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    Cited by:

    1. 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.

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