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Activity Number:
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66
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Type:
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Contributed
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Date/Time:
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Sunday, August 2, 2009 : 4:00 PM to 5:50 PM
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Sponsor:
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IMS
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| Abstract - #303784 |
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Title:
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Modeling Nonhomogeneous Poisson Process with a Periodic or Almost Periodic Intensity Function
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Author(s):
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Nan Shao*+ and Keh-Shin Lii
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Companies:
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University of California, Riverside and University of California, Riverside
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Address:
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Department of Statistics, Riverside, CA, 92521,
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Keywords:
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Periodic or almost periodic intensity function ; non-homogeneous Poisson process ; Bartlett periodogram
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Abstract:
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We propose a model for the analysis of non-stationary point processes with periodic or almost periodic rate of occurrence. The model deals with the arrivals of events which are unequally spaced and show a pattern of periodicity or almost periodicity, such as stock transactions and earthquake, and so on. We model the rate of occurrence of a non-homogeneous Poisson process as the sum of sinusoidal functions. The consistent estimates of frequencies, phases and amplitudes which form the sinusoidal functions are constructed by the Bartlett periodogram. The estimates are shown to be asymptotically normally distributed. The prediction of the next occurrence is carried out and the mean-squared prediction error is calculated by Monte-Carlo integration. Simulations are conducted to illustrate the theoretical results.
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