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Spectra of Some Self-Exciting and Mutually Exciting Point Processes

Alan G. Hawkes
Biometrika
Vol. 58, No. 1 (Apr., 1971), pp. 83-90
Published by: Oxford University Press on behalf of Biometrika Trust
DOI: 10.2307/2334319
Stable URL: http://www.jstor.org/stable/2334319
Page Count: 8
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Spectra of Some Self-Exciting and Mutually Exciting Point Processes
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Abstract

In recent years methods of data analysis for point processes have received some attention, for example, by Cox & Lewis (1966) and Lewis (1964). In particular Bartlett (1963 a,b) has introduced methods of analysis based on the point spectrum. Theoretical models are relatively sparse. In this paper the theoretical properties of a class of processes with particular reference to the point spectrum or corresponding covariance density functions are discussed. A particular result is a self-exciting process with the same second-order properties as a certain doubly stochastic process. These are not distinguishable by methods of data analysis based on these properties.

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