A blind method for the estimation of the Hurst exponent in time series: theory and application.
Nowadays many methods for the estimation of self-similarity (Hurst coefficient, H) in time series are available. Most of them, even if very effective, need some a priori information to be applied. We analyzed the eight most used methods for H estimation (working both in time and in frequency). We tested these methods on data generated with four kinds of time series models (fBm and fGn generated iteratively with Feder algorithm, 1f(alpha), and the fractional autoregressive integrated moving-average) in the range 0.1<or=H<or=0.9. We evaluated the performances of each method in terms of accuracy (bias) and precision [standard deviation (STD)] of the deviation from the expected value. The paper proposes a procedure useful for a reliable estimation of H, using these existing methods, without any assumptions on the stationarity/nonstationarity of the time series, where for these types of processes the "nonstationarity" is mainly caused by the divergence of the variance with time. This procedure suggests that one performs, as a first step, the detrended fluctuations analysis, which provides an indication about stationarity of the series and is related to the properties of self-similarity and long correlations. The procedure then identifies the best method for the estimation of H, depending on this first estimation. As an example application, we use our procedure to evaluate the Hurst coefficient in microelectrode array neuronal recordings.
Esposti
Federico
F
Dipartimento di Bioingegneria, Politecnico di Milano, p.zza Leonardo da Vinci, 20133 Milano, Italy. federico.esposti@polimi.it
Ferrario
Manuela
M
Signorini
Maria Gabriella
MG
D000465:Algorithms; D003198:Computer Simulation; D005246:Feedback; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*; D012815:Signal Processing, Computer-Assisted