The difference-sign runs length distribution in testing for serial independence

Abstract

We investigate the sequence of difference-sign runs length of a time series in the context of non-parametric tests for serial independence. This sequence is, under suitable conditioning, a stationary sequence and we prove that the normalized correlation of two consecutive runs length is small (≈0.0427). We use this result in a test based on the relative entropy of the empirical distribution of the runs length. We investigate the performance of the test in simulated series and test serial independence of cardiac data series in atrial fibrillation.

Keywords:

• runs test
• difference-sign
• serial independence
• entropy
• time series
• atrial fibrillation

2000 Mathematics Subject Classification :

• 62G10
• 62M10

Acknowledgements

We thank Mario Curione (Clinical Science Department, University of Rome ‘La Sapienza’ ) for providing data and for valuable discussions. We thank the referees for stimulating criticism.