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Theoretical and Methodological Issues in Serial Correlation Analysis

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Progress in Motor Control

Part of the book series: Advances in Experimental Medicine and Biology ((volume 782))

Abstract

In this chapter, we present some theoretical and methodological problems related to the analysis of serial correlations in experimental data. A very common observation in behavioral and physiological experiments is the presence of long-range correlations in time series. In this case, the current observation seems to keep the memory of a large set of previous observations. This kind of process has been referred to as long-range dependence, long-term memory, fractal correlation, or 1/f noise. There is now a general agreement for considering long-range correlations as reflecting the complexity of the system, defined as the flexible and adaptable coordination between its multiple components and subsystems. Long-range correlations are supposed to sign an optimal compromise between order and disorder; order reflecting a too strict and rigid coordination and disorder the absence of coordination. Long-range correlations are considered the signature of health and adaptability, and deviations towards order and disorder have been described in elderly or pathological populations. As such, the detection of long-range correlations and the assessment of their alteration in specific populations or situations appear as an important scientific goal.

However, the detection of long-range correlation in empirical series is not straightforward. A number of recent experiments have showed that the pattern of correlation observed in empirical series combines short-range and long-range correlation processes. This is important because apparent alterations in long-range correlations could in fact be due to the superimposition of short-term correlation processes.

An additional problem is that short-range correlation processes can sometimes mimic long-range correlations. Classical methods, such as Detrended Fluctuation Analysis or Power Spectrum Density analysis, seem unable to distinguish between short- and long-range correlated processes. Some specific methods have been developed for testing the effective presence of long-range correlations in experimental series.

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Notes

  1. 1.

    Note that we just define a time series as a series of data ordered in time. A strict definition supposes that successive data are spaced by regular time intervals, but in most experiments the series are simply composed of ordered data.

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Authors and Affiliations

  1. EA 2991 Movement to Health - Euromov, UFR STAPS, University Montpellier 1, 700 avenue du Pic Saint Loup, 34090, Montpellier, France

    Didier Delignières & Vivien Marmelat

Authors
  1. Didier Delignières
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  2. Vivien Marmelat
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Corresponding author

Correspondence to Didier Delignières .

Editor information

Editors and Affiliations

  1. University of Cincinnati, N/A, Cincinnati, 45208, Ohio, USA

    Michael J. Richardson

  2. University of Cincinnati, N/A, Cincinnati, 45208, Ohio, USA

    Michael A. Riley

  3. University of Cincinnati, Cincinnati, 45208, Ohio, USA

    Kevin Shockley

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Delignières, D., Marmelat, V. (2013). Theoretical and Methodological Issues in Serial Correlation Analysis. In: Richardson, M., Riley, M., Shockley, K. (eds) Progress in Motor Control. Advances in Experimental Medicine and Biology, vol 782. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5465-6_7

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