| Library: | times |
| See also: | distance |
| Quantlet: | corrint | |
| Description: | Computes the correlation integral for time series. The instantaneous state of a dynamical system is characterized by a point in phase space. A sequence of such states subsequent in time defines the phase space trajectory. If the system is governed by deterministic laws, then after a while, it will arrive at a permanent state regime. This fact is reflected by the convergence of ensembles of phase space trajectories towards an invariant subset of phase space, the attractor of the system. The output of Correlation integral depends on the given radii of the phase space neighbourhood and the embedding dimension and is plotted logarithmically against log(epsilon). |
| Usage: | y = corrint(x,m) | |
| Input: | ||
| x | vector | |
| m | positive integer < 10 (embedding dimension) | |
| Output: | ||
| y | array (first column: log epsilon, second column: log correlation integral) | |
library("times")
randomize(0)
x=normal(100)
y=corrint(x,2)
y[1:2,1:2]
Contents of _tmp (first two lines of y) [1,] -0.67811 -1.0089 [2,] -0.6487 -0.99557
library("times")
dax=read("dax")
daxreturn=tdiff(log(dax))
y=corrint(dax,2)
d=dim(y)
disp=createdisplay(2,1)
title1="Plot of log-Epsilon"
title2="Plot of Correlation Integral"
show(disp,1,1,(y[,1:d[1]]))
show(disp,2,1,(y[,2:d[1]]))
setgopt(disp,1,1,"title", title1)
setgopt(disp,2,1,"title", title2)
"For reading convenience the graphical output has been omitted."