Recursive Kernel Estimation of the Conditional Intensity of Nonstationary Point Processes

This paper develops adaptive nonparametric methods for analyzing seismic data. Kernel smoothing techniques are suitable for space-time point processes; however, they must be adapted to deal with the nonstationarity of earthquakes. By this we mean changes in the spatial and temporal pattern of point occurrences. A class of recursive kernel density and regression estimators are proposed to study the space-time evolution of earthquakes. Their smoothing coefficients can be designed in an optimal way with prediction error criteria. The entire method is naturally oriented to forecasting. An extensive application to the Northern California Earthquake Catalog (NCEC) data-set, and a simulation experiment illustrates and checks the approach.