Asymptotic theory for curve-crossing analysis

Zhibiao Zhao, Wei Biao Wu

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)862-877
Number of pages16
JournalStochastic Processes and their Applications
Issue number7
StatePublished - Jul 2007

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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