Torre Kjerstin, Delignières Didier, Lemoine Loïc
EA 2991 Motor Efficiency and Deficiency, University Montpellier 1, France.
Br J Math Stat Psychol. 2007 May;60(Pt 1):85-106. doi: 10.1348/000711005X89513.
We evaluate the performance of autoregressive, fractionally integrated, moving average (ARFIMA) modelling for detecting long-range dependence and estimating fractal exponents. More specifically, we test the procedure proposed by Wagenmakers, Farrell, and Ratcliff, and compare the results obtained with the Akaike information criterion (AIC) and the Bayes information criterion (BIC). The present studies show that ARFIMA modelling is able to adequately detect long-range dependence in simulated fractal series. Conversely, this method tends to produce a non-negligible rate of false detections in pure autoregressive and moving average (ARMA) series. Generally, ARFIMA modelling has a bias favouring the detection of long-range dependence. AIC and BIC gave dissimilar results, due to the different weights attributed by the two criteria to accuracy and parsimony. Finally, ARFIMA modelling provides good estimates of fractal exponents, and could adequately complement classical methods, such as spectral analysis, detrended fluctuation analysis or rescaled range analysis.
我们评估自回归分数整合移动平均（ARFIMA）模型在检测长程相关性和估计分形指数方面的性能。更具体地说，我们测试了由瓦根梅克斯、法雷尔和拉特克利夫提出的程序，并将所得结果与赤池信息准则（AIC）和贝叶斯信息准则（BIC）进行比较。目前的研究表明，ARFIMA模型能够充分检测模拟分形序列中的长程相关性。相反，在纯自回归和移动平均（ARMA）序列中，该方法往往会产生不可忽略的误检率。一般来说，ARFIMA模型存在偏向于检测长程相关性的偏差。由于这两个准则对准确性和简约性赋予了不同权重，AIC和BIC给出了不同的结果。最后，ARFIMA模型能够很好地估计分形指数，并且可以充分补充经典方法，如频谱分析、去趋势波动分析或重标极差分析。
