Authors: Torre, Kjerstin¹; Delignières, Didier¹; Lemoine, Loïc¹

Source: British Journal of Mathematical and Statistical Psychology, Volume 60, Number 1, May 2007 , pp. 85-106(22)

Abstract:

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.

Document Type: Research article

DOI: 10.1348/000711005X89513

Affiliations: 1: EA 2991 Motor Efficiency and Deficiency, University Montpellier I, France