计算机工程与应用2016，Vol.52Issue(22)：33-38,6.DOI:10.3778/j.issn.1002-8331.1605-0179
一维时间序列分形维数算法对比分析
Performance comparison of methods for estimating fractal di-mension of time series
摘要
Abstract
Fractal dimension is used broadly in fractal analysis for time series. Lots of calculating methods are available, but fully comparison of them is rarely reported in literature. In this study, the most common methods of estimating the fractal dimension for time series directly in the time domain are analyzed and compared over synthetic data(WCF time series). The accuracy, efficiency and dependence on data length are evaluated for each method. Simulation and measurement results indicate that the FA, DFA and Higuchi methods outperform others in accuracy comparison. When it comes to efficiency, Katz, Sevcik and Castiglioni methods have the highest performance. In analysis of dependence on data length, 4,096 is found to be the just length with which most methods could get a stable estimating value. Especially for FA, DFA and Higuchi methods, whose estimated value coincide with theory value well. Therefore, the Higuchi and DFA methods outshine than others in calculating fractal dimension, and they should be taken precedence in related computing.关键词
分形维数/Higuchi/去趋势波动分析/波动分析/准确性/效率/数据长度Key words
fractal dimension/Higuchi/Detrended Fluctuation Analysis(DFA)/Fluctuation Analysis(FA)/accuracy/efficiency/data length分类
信息技术与安全科学引用本文复制引用
秦建强,孔祥玉,胡绍林,马红光..一维时间序列分形维数算法对比分析[J].计算机工程与应用,2016,52(22):33-38,6.基金项目
国家自然科学基金面上项目（No.61174207，No.61374120）。 （）
