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In order to interpret and explain the physiological signal behaviors, it canbe interesting to find some constants among the fluctuations of these dataduring all the effort or during different stages of the race (which can bedetected using a change points detection method). Several recent papers haveproposed the long-range dependence (Hurst) parameter as such a constant.However, their results induce two main problems. Firstly, DFA method is usuallyapplied for estimating this parameter. Clearly, such a method does not providethe most efficient estimator and moreover it is not at all robust even in thecase of smooth trends. Secondly, this method often gives estimated Hurstparameters larger than 1, which is the larger possible value for long memorystationary processes. In this article we propose solutions for both theseproblems and we define a new model allowing such estimated parameters.

A new stochastic process to model Heart Rate series during exhaustive run and an estimator of its fractality parameter