Title :
Asymptotic Properties of the Detrended Fluctuation Analysis of Long-Range-Dependent Processes
Author :
Bardet, Jean-Marc ; Kammoun, Imen
Author_Institution :
Univ. of Paris 1, Paris
fDate :
5/1/2008 12:00:00 AM
Abstract :
In the past few years, a certain number of authors have proposed analysis methods of the time series built from a long-range dependence noise. One of these methods is the detrended fluctuation analysis (DFA), frequently used in the case of physiological data processing. The aim of this method is to highlight the long-range dependence of a time series with trend. In this paper, asymptotic properties of the DFA of the fractional Gaussian noise (FGN) are provided. Those results are also extended to a general class of stationary long-range-dependent processes. As a consequence, the convergence of the semiparametric estimator of the Hurst parameter is established. However, several simple examples also show that this method is not at all robust in the case of trends.
Keywords :
Gaussian noise; estimation theory; time series; Hurst parameter; detrended fluctuation analysis; fractional Gaussian noise; long-range-dependent processes; physiological data processing; semiparametric estimator convergence; time series; 1f noise; Convergence; Data processing; Doped fiber amplifiers; Fluctuations; Gaussian noise; Noise robustness; Signal analysis; Signal processing; Time series analysis; Detrended fluctuation analysis (DFA); Hurst parameter; fractional Gaussian noise (FGN); long-range-dependent processes; self-similar process; stationary process; trend;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2008.920328