TY - JOUR
T1 - Relative roughness
T2 - An index for testing the suitability of the monofractal model
AU - Marmelat, Vivien
AU - Torre, Kjerstin
AU - Delignières, Didier
PY - 2012
Y1 - 2012
N2 - Fractal analyses have become very popular and have been applied on a wide variety of empirical time series. The application of these methods supposes that the monofractal framework can offer a suitable model for the analyzed series. However, this model takes into account a quite specific kind of fluctuations, and we consider that fractal analyses have been often applied to series that were completely outside of its relevance. The problem is that fractal methods can be applied to all types of series, and they always give a result, that one can then erroneously interpret in the context of the monofractal framework. We propose in this paper an easily computable index, the relative roughness (RR), defined as the ratio between local and global variances, that allows to test for the applicability of fractal analyses. We show that RR is confined within a limited range (between 1.21 and 0.12, approximately) for long-range correlated series. We propose some examples of empirical series that have been recently analyzed using fractal methods, but, with respect to their RR, should not have been considered in the monofractal model. An acceptable level of RR, however, is a necessary but not sufficient condition for considering series as long-range correlated. Specific methods should be used in complement for testing for the effective presence of long-range correlations in empirical series.
AB - Fractal analyses have become very popular and have been applied on a wide variety of empirical time series. The application of these methods supposes that the monofractal framework can offer a suitable model for the analyzed series. However, this model takes into account a quite specific kind of fluctuations, and we consider that fractal analyses have been often applied to series that were completely outside of its relevance. The problem is that fractal methods can be applied to all types of series, and they always give a result, that one can then erroneously interpret in the context of the monofractal framework. We propose in this paper an easily computable index, the relative roughness (RR), defined as the ratio between local and global variances, that allows to test for the applicability of fractal analyses. We show that RR is confined within a limited range (between 1.21 and 0.12, approximately) for long-range correlated series. We propose some examples of empirical series that have been recently analyzed using fractal methods, but, with respect to their RR, should not have been considered in the monofractal model. An acceptable level of RR, however, is a necessary but not sufficient condition for considering series as long-range correlated. Specific methods should be used in complement for testing for the effective presence of long-range correlations in empirical series.
KW - Monofractal model, long-range correlations, relative roughness
UR - http://www.scopus.com/inward/record.url?scp=84866350458&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84866350458&partnerID=8YFLogxK
U2 - 10.3389/fphys.2012.00208
DO - 10.3389/fphys.2012.00208
M3 - Article
C2 - 22719731
AN - SCOPUS:84866350458
VL - 3 JUN
JO - Frontiers in Physiology
JF - Frontiers in Physiology
SN - 1664-042X
M1 - Article 208
ER -