Lee Chang-Yong
Department of Industrial and Systems Engineering, Kongju National University, Kongju 314-701, South Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jul;86(1 Pt 1):011135. doi: 10.1103/PhysRevE.86.011135. Epub 2012 Jul 30.
We propose a methodology of estimating the scaling exponent for a long-range correlation in a nonstationary time series from the perspective of the regression analysis. By an adaptive degree determination of a regression polynomial, the proposed methodology is designed to properly remove various types of trends embedded in the nonstationary signal so that the scaling exponent can be estimated without artificial crossovers. To show the validity of the proposed methodology, we applied it to the detrended fluctuation analysis and tested it out against correlated data superimposed by various types of trends. It turned out that, unlike the conventional technique, our approach was capable of eliminating artificial crossovers. We also discuss the statistical characteristics of the proposed method with regard to the estimation of the scaling exponent.
我们从回归分析的角度提出了一种用于估计非平稳时间序列中长程相关性的标度指数的方法。通过对回归多项式的自适应阶数确定，所提出的方法旨在适当地去除嵌入在非平稳信号中的各种类型的趋势，从而可以在没有人为交叉的情况下估计标度指数。为了证明所提出方法的有效性，我们将其应用于去趋势波动分析，并针对叠加了各种类型趋势的相关数据对其进行了测试。结果表明，与传统技术不同，我们的方法能够消除人为交叉。我们还讨论了所提出方法在标度指数估计方面的统计特性。
