spaceTime {fractal} | R Documentation |
This function can be used to generate contours of a space time separation plot. This plot type is a visual tool which can help to determine the correlation time for a particular delay embedding of a given time series.
spaceTime(x, dimension=2, tlag=timeLag(x, method="acfdecor"), olag.max=as.integer(min(500,length(x)/20)), probability=0.1)
x |
a vector holding a scalar time series |
dimension |
the desired embedding dimension. Default: 2 . |
olag.max |
an integer representing the maximum orbital lag
ot use in forming the results. Default: as.integer(min(500,length(x)/20)) . |
probability |
a positive numeric scalar on the interval (0,1) which
gives the probability associated with the first contour. This input
determines the number of contours to be generated (see the output
description below). Default: 0.1 . |
tlag |
the delay used to create the delay embedding. Default: timeLag(x, method="acfdecor") . |
Each contour, C(p,dt), in a space time separation plot corresponds to a particular probability, p, and gives spatial distance between pairs of phase space vectors as a function of their temporal separation. In particular, any pair of vectors seperated in time by dt are separated in the phase space by distance C(p,dt) with probability p.
an object of class spaceTime
.
par
function. Default: "l"
(solid line).polygon
function. Default: 10
.TRUE
, the plot is added using the current par
settings.
Otherwise, the par
settings are adjusted as needed. Default: FALSE
.par
function.spaceTime
object.
Optional arguments include:
par
function. Default: 1
.1:8
."Orbital Lag"
."Spatial Separation"
.NULL
(no title).par
. Default: 1
.par
. Default: "."
.TRUE
, the plot is added using the current par
settings.
Otherwise, the par
settings are adjusted as needed. Default: FALSE
.par
function.spaceTime
object.
Holger Kantz and Thomas Schreiber, Nonlinear Time Series Analysis, Cambridge University Press, 1997.
embedSeries
, determinism
, timeLag
.
## Using the beamchaos data calculate the space ## time separation contours for probabilities ## 1/10, 2/10, ..., 1, for a 3-dimensional ## delay embedding with delay of 10. Plot the ## resulting contours, which will reveal ## periodicity in the data. From the top ## contour in the plot, which corresponds to ## probability 1, we can conclude that any two ## vectors in the chosen delay embedding which ## are separated in time by approximately 90 ## time steps are separated by a distance of at ## least 8 in the phase space. z <- spaceTime(beamchaos, dim=3, tlag=10, olag.max=500, probability=1/10) ## print the results print(z) ## plot the results plot(z) ## extended data analysis plot eda.plot(z)