In chaos theory, the correlation sum is the estimator of the correlation integral, which reflects the mean probability that the states at two different times are close:

a norm (e.g. Euclidean norm the Heaviside step function. If only a time series is available, the phase space can be reconstructed by using a time delay embedding (see Takens' theorem):

the time delay.

The correlation sum is used to estimate the correlation dimension.

See also

• Recurrence quantification analysis

References