Asymptotic theory for curve-crossing analysis
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.
Year of publication: |
2007
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Authors: | Zhao, Zhibiao ; Wu, Wei Biao |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 117.2007, 7, p. 862-877
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Publisher: |
Elsevier |
Keywords: | Central limit theorem Curve-crossing Linear processes Multiple Wiener-Ito integral Non-central limit theorem Nonlinear time series |
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