© 1992 by Biometrika Trust
A dynamic approach to the statistical analysis of point processes
Departamento de Métodos Estatisticos, Instituto de Matemática, Universidade Federal do Rio de Janeiro 21944 Rio de Janeiro, RJ, Brazil
An approach to the analysis of point processes based on sequential analysis of successive intervals assuming a piecewise constant intensity rate is presented. Bayesian inference for processes with explanatory variables is derived in terms of on-line estimation, filtering and prediction. Limiting equations for the time-continuous intensity rate are obtained and solved for the no-covariates case. Examples are provided and the approach is applied in a numerical example.
Key Words: Intensity rate Piecewise self-exciting process Prediction Smoothing Time variation