Comparison of different methods for computing scaling parameter in the presence of trends

In a large number of analysis of biological signals, such as ElectroEncephaloGrams or Heart Rate Variability, phenomena such as long range correlation or long term memory or self similarity or more generally scaling phenomena have been observed and are often used as a basis for diagnosis and the assertion of major physiological facts. It is therefore an important issue to be able to perform a relevant analysis (detection, estimation) of such phenomena on empirical data. For a reliable use of long-range correlation analysis, it is essential to be able to distinguish between trends (whatever their origin - external, apparatus - or internal but related to other biological mechanism such as breathing...) and long-range fluctuations intrinsic to the data. In this paper we compare estimates of the Hurst parameter based on i) Detrending Fluctuation Analysis, ii) wavelet analysis, iii) discrete variations. We discuss their capabilities for a reliable estimation of the scaling exponent, depending on the signal length and for different trends, using simulated and real data.