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Title: Different approaches for testing the independence between point processes Authors:  Ana C Cebrian - University of Zaragoza (Spain) [presenting]
Abstract: Many real problems involve two or more point processes and require a description of their dependence structure, for example the timing of the trades and mid-quote changes in Stock Exchange or the occurrence of climate extremes at different spatial locations. These processes have to be studied in a multivariate point process framework and an important issue to consider is the independence between the marginal processes. Three families of tests to check the independence between point processes, conditionally on their marginal structure, are presented: conditional tests for Poisson processes, tests based on the close point sets and tests based on the $J$ and $K$ functions. Each test is based on different assumptions, and is adequate for different type pf processes: Poisson processes, homogeneous point processes, nonhomogeneous processes with a parametric model, etc. All together cover a wide range of situations and dependence structures. A comparative study of the size and power of the tests is carried out. Future work includes the extension of some of the suggested tests to the case of doubly stochastic point processes.