Asymptotic theory for curve-crossing analysis

Zhibiao Zhao; Wei Biao Wu

doi:10.1016/j.spa.2006.10.010

Asymptotic theory for curve-crossing analysis

Zhibiao Zhao, Wei Biao Wu

Statistics

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4 Scopus citations

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 language	English (US)
Pages (from-to)	862-877
Number of pages	16
Journal	Stochastic Processes and their Applications
Volume	117
Issue number	7
DOIs	https://doi.org/10.1016/j.spa.2006.10.010
State	Published - Jul 2007

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modeling and Simulation
Applied Mathematics

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10.1016/j.spa.2006.10.010

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title = "Asymptotic theory for curve-crossing analysis",

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-It{\^o} integrals or integrals with respect to stable L{\'e}vy processes, depending on the heaviness of tails of the underlying processes.",

author = "Zhibiao Zhao and Wu, {Wei Biao}",

note = "Funding Information: The authors are grateful to the two referees and the associate editor for their many helpful comments. The work is supported in part by NSF grant DMS-0478704.",

year = "2007",

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doi = "10.1016/j.spa.2006.10.010",

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AU - Zhao, Zhibiao

AU - Wu, Wei Biao

N1 - Funding Information: The authors are grateful to the two referees and the associate editor for their many helpful comments. The work is supported in part by NSF grant DMS-0478704.

PY - 2007/7

Y1 - 2007/7

N2 - 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.

AB - 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.

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DO - 10.1016/j.spa.2006.10.010

M3 - Article

AN - SCOPUS:34248585381

SN - 0304-4149

VL - 117

SP - 862

EP - 877

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 7

ER -

Asymptotic theory for curve-crossing analysis

Abstract

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