Theoretical and methodological issues in serial correlation analysis.

We present in this paper 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 sub-systems. 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 shortterm 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 shortand long-range correlated processes. Some specific methods have been developed for testing for the effective presence of long-range correlations in experimental series.