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

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.