A second-order test to detect spatio-temporal anisotropic effects in point patterns

ABSTRACT

Second-order spatio-temporal orientation methods provide a natural tool for the analysis of anisotropic spatio-temporal point process data. In this paper, we generalize a method based on the spatial point pair orientation distribution function to test for evidence of spatio-temporal anisotropy, by exploring the fact that the space–time orientation function is the distribution function of a uniform random variable on $[0,\pi )$ for any second-order intensity reweighted stationary and isotropic spatio-temporal point process. We present a numerical procedure based on this result to test for anisotropic effects, illustrated through a simulation study considering several space–time structures including Poisson and cluster configurations. The resulting testing procedure is applied to analyse the spatio-temporal distribution of earthquakes in Southern California for the period 1984–2004. Our results confirm that our approach is able to detect directional components at distinct spatio-temporal scales.

KEYWORDS:

• Anisotropy
• earthquakes
• K-function
• orientation distribution
• second-order intensity-reweighted
• space–time point patterns

AMS SUBJECT CLASSIFICATION:

• 62M30

Acknowledgments

The authors are grateful to the Associate Editor and the referees whose comments and suggestions have clearly improved an earlier version of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was partially funded by grants MTM2016-78917-R and MTM2017-86767-R from the Spanish Ministry of Economy, Industry and Competitiveness.