Non-parametric smoothing of spatio-temporal point processes

This paper develops adaptive non-parametric modelings for earthquake data. Non-parametric techniques are particularly suitable for space–time point processes, however they must be adapted to deal with the non-stationarity of seismic phenomena. By this we mean changes in the spatial and temporal pattern of seismic occurrences. A set of non-parametric tests, kernel density and regression estimators are proposed to study the space–time evolution of earthquakes. The implied solutions, by respecting the unidirectional nature of time and minimizing prediction errors, are naturally oriented to forecasting. An extensive application to the Northern California Earthquake Catalog (NCEC) data-set, starting from 1930, illustrates and checks the approach.