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

TL;DR

This paper introduces a novel stochastic process model for heart rate series during exhaustive runs and proposes an improved estimator for its fractality parameter, addressing limitations of existing methods like DFA.

Contribution

The paper presents a new stochastic process model and an estimator for the fractality parameter that overcomes DFA's inefficiencies and robustness issues.

Findings

Proposes a new model for heart rate series during exhaustive effort.

Develops an estimator that accurately captures the fractality parameter.

Addresses limitations of DFA, including robustness and parameter bounds.

Abstract

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