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Second-order residual analysis of spatiotemporal point processes and applications in model evaluation. (English) Zbl 1110.62128
Summary: The paper gives a first-order residual analysis for spatiotemporal point processes that is similar to the residual analysis that has been developed by A. Baddeley et al. [ibid. 67, No. 5, 617–666 (2005; Zbl 1112.62302)] for spatial point processes and also proposes principles for second-order residual analysis based on the viewpoint of martingales. Examples are given for both first- and second-order residuals. In particular, residual analysis can be used as a powerful tool in model improvement. Taking a spatiotemporal epidemic-type aftershock sequence model for earthquake occurrences as the base-line model, second-order residual analysis can be useful for identifying many features of the data that are not implied in the base-line model, providing us with clues about how to formulate better models.

MSC:
62M30 Inference from spatial processes
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
86A17 Global dynamics, earthquake problems (MSC2010)
62M99 Inference from stochastic processes
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