Testing independence between two nonhomogeneous point processes in time

Abstract

Point processes are often used to model the occurrence times of different phenomena, such as heatwaves or spike trains. Many of those problems require to study the independence between nonhommogeneous point processes in time, and this work develops three families of tests to assess that hypothesis. They can be applied to different types of processes, and all together they cover a wide range of situations appearing in real problems. The first family includes two tests for Poisson processes. The second family is based on the close point distance, and the third one on cross dependence functions. An extensive simulation study of the size and power of the tests is carried out and some practical rules to select the most appropriate test in different cases, are provided. The proposed tests are demonstrated on a real data application about the occurrence of extreme heat events in three Spanish locations.

Keywords:

• Nonhomogeneous point process
• Poisson process
• test of independence
• bootstrap test

2010 Mathematics Subject Classifications:

• 60Gxx
• 60Hxx
• 62Mxx
• 62Pxx

Acknowledgements

The authors are members of the research group Modelos Estocásticos, supported by Gobierno de Aragón and the European Social Fund and the project MTM2017-83812-P.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The data that support the findings of this study are available from the corresponding author upon request.

Additional information

Funding

The authors are members of the research group Modelos Estocásticos, supported by Gobierno de Aragón and the European Social Fund and the project MTM2017-83812-P.