B0877
Title: Forecasting a compound Cox process
Authors: Carmen Montes-Gijon - Universidad de Granada (Spain) [presenting]
Paula Bouzas - University of Granada (Spain)
Nuria Ruiz-Fuentes - University of Jaen (Spain)
Abstract: The compound Cox process generalizes the Cox process and models several variations of the latter. A Cox process with random deletions, one with simultaneous occurrences, or a time-space Cox process can all be modeled by a compound Cox process. In any of these cases, the points with a given specific mark can be of interest and, thus, the counting process that is formed is equally of interest. This new counting process has been shown to be another Cox process whose statistics are derivable, therefore closed form expressions of the counting and time statistics are given here. Most of these statistics can be expressed in terms of the mean process of the compound Cox process. Using principal components prediction models, the mean, and hence the statistics, can be predicted. In particular, it is possible to forecast the mean number of points with specific marks as well as the mode or the cumulative distribution function. Additionally, the probability of having a new point within an interval of time can also be forecast under weak assumptions, as proven. Simulations of several examples of compound Cox processes illustrate the results.
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