Editing Pearson correlation coefficient (section)

===Scaled correlation coefficient===
{{Main|Scaled correlation}}

Scaled correlation is a variant of Pearson's correlation in which the range of the data is restricted intentionally and in a controlled manner to reveal correlations between fast components in [[time series]].<ref name = "Nikolicetal">{{cite journal | last1 = Nikolić | first1 = D | last2 = Muresan | first2 = RC | last3 = Feng | first3 = W | last4 = Singer | first4 = W | year = 2012 | title = Scaled correlation analysis: a better way to compute a cross-correlogram | url = http://www.danko-nikolic.com/wp-content/uploads/2012/03/Scaled-correlation-analysis.pdf | journal = European Journal of Neuroscience | volume =  35| issue = 5| pages = 1–21 | doi = 10.1111/j.1460-9568.2011.07987.x | pmid = 22324876 | s2cid = 4694570 }}</ref> Scaled correlation is defined as average correlation across short segments of data.

Let <math>K</math> be the number of segments that can fit into the total length of the signal <math>T</math> for a given scale <math>s</math>:

:<math>K = \operatorname{round}\left(\frac{T}{s}\right).</math>

The scaled correlation across the entire signals <math>\bar{r}_s</math> is then computed as

:<math>\bar{r}_s = \frac{1}{K} \sum\limits_{k=1}^K r_k,</math>

where <math>r_k</math> is Pearson's coefficient of correlation for segment <math>k</math>.

By choosing the parameter <math>s</math>, the range of values is reduced and the correlations on long time scale are filtered out, only the correlations on short time scales being revealed. Thus, the contributions of slow components are removed and those of fast components are retained.