Comparison of DFA vs wavelet analysis for estimation of regularity of HR series during the marathon Imen Kammoun a , V´ eronique Billat b , Jean-Marc Bardet a,∗ a Universit´ e Paris 1, SAMOS-MATISSE-CES, 90 rue de Tolbiac, 75013 Paris, France b Universit´ e d’Evry, LEPHE, E.A. 3872 Genopole, Boulevard F. Mitterrand, Evry Cedex, France Abstract In order to interpret and explain the physiological signal behaviors, it can be inter- esting to find some constants among the fluctuations of these data during all the effort or during different stages of the race. These different stages can be detected using a change points detection method. Then, the Hurst parameter of long-range dependence could be a new way for deducing some explanations. Several common estimators of this parameter, so-called scaling behavior exponents, consist in per- forming a linear regression fit of a scale-dependent quantity versus the scale in a log- arithmic representation. This includes the Detrended Fluctuation Analysis (DFA) method and wavelet analysis method. This second method provides more robust results and can be applied to more general models. Then, it permits us the con- struction of the semi-parametric process which could be more relevant than other for modelling HR data. It also shows an evolution of the Hurst parameter during the race, what confirms results obtained by Peng et al. in their study concerning recorded HR time series during the exercise for healthy adults (where the estimated parameter is close to that observed in the race beginning) and heart failure adults (where the estimated parameter is close to that observed in the end of race). So, this evolution, which can not be observed with DFA method, may be associated with fatigue appearing during the last phase of the marathon. Key words: Wavelet analysis, Detrended fluctuation analysis, Fractional Gaussian noise, Self-similarity, Hurst parameter, Long-range dependence processes, Heart rate time series ∗ Corresponding author. Email address: bardet@univ-paris1.fr (Jean-Marc Bardet). Preprint submitted to Elsevier 17 August 2007