Analyzing exact fractal time series: evaluating dispersional analysis and rescaled range methods
Analyzing exact fractal time series: evaluating dispersional analysis and rescaled range methods
复制标题
DOI：
10.1016/s0378-4371(97)00363-4
复制
发表时间：
1997-12-01
期刊：
影响因子：
3.3
通讯作者：
Bassingthwaighte, JB
中科院分区：
文献类型：
--
作者：
Caccia, DC;Percival, D;Bassingthwaighte, JB
需要精确的参考信号来评估用于表征分形时间序列的方法。在这里，我们使用fGp（分数高斯过程）来生成一维时间序列的精确分数高斯噪声（fGn）参考信号。fGn的多个实现的平均自相关收敛到理论上预期的自相关。两种常用的方法来产生分形时间序列，近似谱合成（SSM）的方法和连续随机添加（SRA）的方法，不给正确的相关结构，应该放弃。使用fGp的时间序列来测试几种版本的重标极差分析（RIS）和分散分析（Disp）估计赫斯特系数（0 < H < 1.0）的效果。当H < 0.9且序列长度N大于或等于1024时，Disp是无偏的，但当H > 0.9时，Disp低估了H。R/S-去趋势高估了H 0.7的时间序列的H< 0.7 and underestimates H for H >。所有版本的Disp的H（（H）over cap））估计值通常比R/S的估计值具有更低的偏倚和方差。所有版本的色散分析，Disp，现在在fGp上测试，比我们以前认为的要好，推荐用于评估作为长记忆过程的时间序列。
Precise reference signals are required to evaluate methods for characterizing a fractal time series. Here we use fGp (fractional Gaussian process) to generate exact fractional Gaussian noise (fGn) reference signals for one-dimensional time series. The average autocorrelation of multiple realizations of fGn converges to the theoretically expected autocorrelation. Two methods commonly used to generate fractal time series, an approximate spectral synthesis (SSM) method and the successive random addition (SRA) method, do not give the correct correlation structures and should be abandoned. Time series from fGp were used to test how well several versions of rescaled range analysis (RIS) and dispersional analysis (Disp) estimate the Hurst coefficient(0 < H < 1.0). Disp is unbiased for H < 0.9 and series length N greater than or equal to 1024, but underestimates H when H > 0.9. R/S-detrended overestimates H for time series with H < 0.7 and underestimates H for H > 0.7. Estimates of H((H) over cap)) from all versions of Disp usually have lower bias and variance than those from R/S. All versions of dispersional analysis, Disp, now tested on fGp, are better than we previously thought and are recommended for evaluating time series as long-memory processes.