TY - JOUR
T1 - Asymptotic theory for curve-crossing analysis
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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U2 - 10.1016/j.spa.2006.10.010
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 -