d2 function

Sample correlation integral (at multiple length scales)

Computes the sample correlation integral over a grid of neps length scales starting from eps.min, and for multiple embedding dimensions

d2(series, m, d, t, eps.min, neps=100)

Arguments

• series: time series
• m: max embedding dimension
• d: time delay
• t: Theiler window
• eps.min: min length scale
• neps: number of length scales to evaluate

Details

Computes the sample correlation integral over neps length scales starting from eps.min, for embedding dimension 1, ,m , considering a t time window (see references). The slope of the linear segment in the log-log plot gives an estimate of the correlation dimension (see the example).

Returns

Matrix. Column 1: length scales. Column i=2, , m+1: sample correlation integral for embedding dimension i-1.

Examples

d2(lorenz.ts, m=6, d=2, t=4, eps.min=2)

References

Hegger, R., Kantz, H., Schreiber, T., Practical implementation of nonlinear time series methods: The TISEAN package; CHAOS 9, 413-435 (1999)

Author(s)

Antonio, Fabio Di Narzo