文献类型：期刊文献

英文题名：EFFECTS OF POLYNOMIAL TRENDS ON DETRENDING MOVING AVERAGE ANALYSIS

作者：Shao, Ying-Hui[1,2];Gu, Gao-Feng[1,2];Jiang, Zhi-Qiang[1,2];Zhou, Wei-Xing[1,2,3]

机构：[1]E China Univ Sci & Technol, Sch Business, Shanghai 200237, Peoples R China;[2]E China Univ Sci & Technol, Res Ctr Econophys, Shanghai 200237, Peoples R China;[3]E China Univ Sci & Technol, Sch Sci, Shanghai 200237, Peoples R China

年份：2015

卷号：23

期号：3

外文期刊名：FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY

收录：;EI(收录号：20153201113249);WOS:【SCI-EXPANDED(收录号:WOS:000358787500013)】；

基金：We acknowledge financial support from the National Natural Science Foundation of China Grant No. 11375064 and the Fundamental Research Funds for the Central Universities.

语种：英文

外文关键词：Fractal Analysis; Detrending Moving Average (DMA); Scaling Law; Crossover Behavior; Polynomial Trend; Constant Shift; Linear Trend

摘要：The detrending moving average (DMA) algorithm is one of the best performing methods to quantify the long-term correlations in nonstationary time series. As many long-term correlated time series in real systems contain various trends, we investigate the effects of polynomial trends on the scaling behaviors and the performances of three widely used DMA methods including backward algorithm (BDMA), centered algorithm (CDMA) and forward algorithm (FDMA). We derive a general framework for polynomial trends and obtain analytical results for constant shifts and linear trends. We find that the behavior of the CDMA method is not influenced by constant shifts. In contrast, linear trends cause a crossover in the CDMA fluctuation functions. We also find that constant shifts and linear trends cause crossovers in the fluctuation functions obtained from the BDMA and FDMA methods. When a crossover exists, the scaling behavior at small scales comes from the intrinsic time series while that at large scales is dominated by the constant shifts or linear trends. We also derive analytically the expressions of crossover scales and show that the crossover scale depends on the strength of the polynomial trends, the Hurst index, and in some cases (linear trends for BDMA and FDMA) the length of the time series. In all cases, the BDMA and the FDMA behave almost the same under the influence of constant shifts or linear trends. Extensive numerical experiments confirm excellently the analytical derivations. We conclude that the CDMA method outperforms the BDMA and FDMA methods in the presence of polynomial trends.