Limits...
Relative roughness: an index for testing the suitability of the monofractal model.

Marmelat V, Torre K, Delignières D - Front Physiol (2012)

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Movement to Health, University Montpellier 1 Montpellier, France.

ABSTRACT
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.

No MeSH data available.


Related in: MedlinePlus

Top: an example series of center-of-pressure velocity, during the maintenance of upright posture (sampling frequency: 40 Hz). The dashed lines represent the upper and lower limits that bound the evolution of the series. Bottom: average DFA diffusion plot (left) and average log–log power spectrum (right). From Delignières et al. (2011a).
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Figure 7: Top: an example series of center-of-pressure velocity, during the maintenance of upright posture (sampling frequency: 40 Hz). The dashed lines represent the upper and lower limits that bound the evolution of the series. Bottom: average DFA diffusion plot (left) and average log–log power spectrum (right). From Delignières et al. (2011a).

Mentions: This problem was recently considered by Delignières et al. (2011a), in the domain of postural control. Research on postural control focuses on the analysis of center-of-pressure (COP) trajectory, easily recorded with force platforms. A number of authors, during the last decade, have proposed to apply to these data diverse non-linear methods, including fractal analyses. Delignières et al. (2011a) formulated strong reserves about the suitability of the fractal framework for modeling COP data, which appear clearly bounded within functional limits. Interestingly, they showed that bounding affected primarily COP velocity, rather than COP position series, as generally accepted in the literature (Collins and De Luca, 1993). This result suggested that bounding could be due to motor control limitations, rather than by biomechanical constraints as commonly assumed. We present in Figure 7 (top row) an example COP velocity series, sampled at 40 Hz, that illustrates this bounding phenomenon: COP velocity presents highly persistent trends on the short-term, but these trends tend to reverse in direction when velocity reaches the upper or the lower limits represented by the dashed lines.


Relative roughness: an index for testing the suitability of the monofractal model.

Marmelat V, Torre K, Delignières D - Front Physiol (2012)

Top: an example series of center-of-pressure velocity, during the maintenance of upright posture (sampling frequency: 40 Hz). The dashed lines represent the upper and lower limits that bound the evolution of the series. Bottom: average DFA diffusion plot (left) and average log–log power spectrum (right). From Delignières et al. (2011a).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3376770&req=5

Figure 7: Top: an example series of center-of-pressure velocity, during the maintenance of upright posture (sampling frequency: 40 Hz). The dashed lines represent the upper and lower limits that bound the evolution of the series. Bottom: average DFA diffusion plot (left) and average log–log power spectrum (right). From Delignières et al. (2011a).
Mentions: This problem was recently considered by Delignières et al. (2011a), in the domain of postural control. Research on postural control focuses on the analysis of center-of-pressure (COP) trajectory, easily recorded with force platforms. A number of authors, during the last decade, have proposed to apply to these data diverse non-linear methods, including fractal analyses. Delignières et al. (2011a) formulated strong reserves about the suitability of the fractal framework for modeling COP data, which appear clearly bounded within functional limits. Interestingly, they showed that bounding affected primarily COP velocity, rather than COP position series, as generally accepted in the literature (Collins and De Luca, 1993). This result suggested that bounding could be due to motor control limitations, rather than by biomechanical constraints as commonly assumed. We present in Figure 7 (top row) an example COP velocity series, sampled at 40 Hz, that illustrates this bounding phenomenon: COP velocity presents highly persistent trends on the short-term, but these trends tend to reverse in direction when velocity reaches the upper or the lower limits represented by the dashed lines.

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Movement to Health, University Montpellier 1 Montpellier, France.

ABSTRACT
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.

No MeSH data available.


Related in: MedlinePlus