Pearson Correlation Coefficient

Pearson correlation coefficient (or Pearson coefficient) between x and y is defined by:

Cov[x,y]/(Var[x]Var[y])1/2

where Cov(x,y) is covariance and Var(x) is variance.

For the forex time series we analyze, the mean is typically at least two orders of magnitude smaller than the RMS. For this reason we often neglect the mean. Then, Cov[x,y] is simply the amplitude of the zero-lag bin of the cross-correlation function and Var[x] is the amplitude of the zero-lag bin of the autocorrelation function. When dealing with covariance alone, one does not know whether its change reflect the change in the strength of correlation between x and y or in strength of their independent variation. Pearson correlation coefficient allows one to analyse the tightness of the correlation between two quantities as such, leaving aside the question of the overall strength of their variation (correlated or not).