Definition of distance for nonlinear time series analysis of marked point process data

Marked point process data are time series of discrete events accompanied with some values, such as economic trades, earthquakes, and lightnings. A distance for marked point process data allows us to apply nonlinear time series analysis to such data. We propose a distance for marked point process data which can be calculated much faster than the existing distance when the number of marks is small. Furthermore, under some assumptions, the Kullback-Leibler divergences between posterior distributions for neighbors defined by this distance are small. We performed some numerical simulations showing that analysis based on the proposed distance is effective.