Asymptotic theory for curve-crossing analysis

Zhibiao Zhao, Wei Biao Wu

Research output: Contribution to journalArticle

4 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)862-877
Number of pages16
JournalStochastic Processes and their Applications
Volume117
Issue number7
DOIs
StatePublished - Jul 1 2007

Fingerprint

Asymptotic Theory
Time series
Curve
Count
Nonlinear Time Series
Long-range Dependence
Linear Process
Stable Process
Central limit theorem
Asymptotic distribution
Asymptotic Properties
Tail
Dependent
Range of data

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

Cite this

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Asymptotic theory for curve-crossing analysis. / Zhao, Zhibiao; Wu, Wei Biao.

In: Stochastic Processes and their Applications, Vol. 117, No. 7, 01.07.2007, p. 862-877.

Research output: Contribution to journalArticle

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