Coronado Ana V, Carpena Pedro
Departamento de Física Aplicada II, E.T.S.I. de Telecomunicación, Universidad de Málaga, 29071 Málaga, Spain.
J Biol Phys. 2005 Jan;31(1):121-33. doi: 10.1007/s10867-005-3126-8.
The detection and quantification of long-range correlations in time series is a fundamental tool to characterize the properties of different dynamical systems, and is applied in many different fields, including physics, biology or engineering. Due to the diversity of applications, many techniques for measuring correlations have been designed. Here, we study systematically the influence of the length of a time series on the results obtained from several techniques commonly used to detect and quantify long-range correlations: the autocorrelation analysis, Hurst's analysis, and detrended fluctuation analysis (DFA). Using the Fourier filtering method, we generate artificial time series with known and controlled long-range correlations and with a broad range of lengths, and apply on them the different correlation measures we have studied. Our results indicate that while the DFA method is practically unaffected by the length of the time series, and almost always provides accurate results, the results from Hurst's analysis and the autocorrelation analysis strongly depend on the length of the time series.
时间序列中长程相关性的检测与量化是表征不同动力系统特性的一项基本工具，并且应用于许多不同领域，包括物理、生物或工程学。由于应用的多样性，人们设计了许多测量相关性的技术。在此，我们系统地研究了时间序列长度对几种常用于检测和量化长程相关性的技术所得结果的影响：自相关分析、赫斯特分析和去趋势波动分析（DFA）。我们使用傅里叶滤波方法生成具有已知且可控长程相关性以及广泛长度范围的人工时间序列，并将我们研究的不同相关性度量应用于这些序列。我们的结果表明，虽然DFA方法实际上不受时间序列长度的影响，并且几乎总能提供准确结果，但赫斯特分析和自相关分析的结果强烈依赖于时间序列的长度。
