Correlation sum
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:
where is the number of considered states, is a threshold distance, a norm and the Heaviside step function. If only a time series is available, the phase space can be reconstructed by using a time delay embedding :
where is the time series, the embedding dimension and the time delay.
The correlation sum is used to estimate the correlation dimension.
