No. 966

Title:

Second-order residual analysis of spatio-temporal point processes and applications in model evolution

Author(s):

Zhuang, Jiancang (Institute of Statistical Methematics)

Key words:

Residual analysis; point process; martingale; predictable process; ETAS model; second-order residual analysis; model evolution.

Abstract:

    This paper overviews the first-order residual analysis for point processes developed by Baddeley et al.(2005), and then proposes the principles for the second-order martingale based residual analysis. Examples are given for both first- and second-order residuals. In particular, second-order residual analysis can be used as a powerful tool in model evolution. Taking the spatio-temporal epidemic-type aftershock sequence (ETAS) model for earthquake occurrences as the baseline model, second-order residual analysis can be useful to identify many features of the data not implied in the baseline model, providing us with clues of how to formulate better models.