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Measuring the association of a time series and a point process

Published online by Cambridge University Press:  14 July 2016

J. S. Willie
J. S. Willie*
Affiliation:
Bell Laboratories
*
∗Postal address: 2F-18, Bell Laboratories, 11900 N. Pecos St., Denver, CO 80234, U.S.A.
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Abstract

We consider a bivariate stochastic process where one component is an ordinary time series and the other is a point process. In the stationary case, a useful measure of the association of the time series and the point process is provided by a conditional intensity function, ṙ11(x;u), which gives the intensity with which events occur near time t given that the time series takes on a value x at time t + u. In this paper we consider the estimation of the function ṙ11(x;u) and certain related functions that are also useful in partially characterizing the degree of interdependence of the time series and the point process. Histogram and smoothed histogram-type estimates are proposed and asymptotic distributions of these estimates are derived. We also discuss an application of the estimation theory to the analysis of some data from a neurophysiological study.

Keywords

ASYMPTOTIC NORMALITYCUMULANTNEUROPHYSIOLOGYNON-PARAMETRIC DENSITY ESTIMATIONSTATIONARY PROCESSSQUARE ROOT TRANSFORMATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 19 , Issue 3 , September 1982 , pp. 597 - 608
Copyright
Copyright © Applied Probability Trust 1982 

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