fractal (version 2.0-4)

spaceTime: Space time separation plot

Description

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.

Usage

spaceTime(x, dimension=2, tlag=timeLag(x, method="acfdecor"),
    olag.max=as.integer(min(500,length(x)/20)), probability=0.1)

Arguments

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").

Value

an object of class spaceTime.

S3 METHODS

as.matrix

convert the output to a matrix.

eda.plot

plot a summary of the space-time contours including a density function estimate of the median contour in addition to a suggested range of suitable orbital lags. In the latter case, the most populous values of the median contour are highlighted by a cross-hatched area that covers a plot of the median curve. The suggested range for a suitable orbital lag is based on the range of values that first escape this cross-hatched region. Optional parameters include:

type

An integer denoting the type of line to plot ala the par function. Default: "l" (solid line).

density

The density of the cross-hatched area ala the polygon function. Default: 10.

add

A logical flag. If TRUE, the plot is added using the current par settings. Otherwise, the par settings are adjusted as needed. Default: FALSE.

...

Additional parameters sent directly to the par function.

plot

plot the space-time contours for the given spaceTime object. Optional arguments include:

lty

Line type ala the par function. Default: 1.

color

A vector of integers defining the contour line colors. Default: 1:8.

xlab

A character string denoting the x-axis label. Default: "Orbital Lag".

ylab

A character string denoting the y-axis label. Default: "Spatial Separation".

main

A character string denoting the title label. Default: NULL (no title).

cex

Character expansion value ala par. Default: 1.

pch

An integer representing the plot character ala par. Default: ".".

add

A logical flag. If TRUE, the plot is added using the current par settings. Otherwise, the par settings are adjusted as needed. Default: FALSE.

...

Additional parameters sent directly to the par function.

print

print a summary of the spaceTime object.

Details

Each contour, \(C_p(\Delta t)\), 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 \(\Delta t\) are separated in the phase space by distance \(C_p(\Delta t)\) with probability \(p\).

References

Holger Kantz and Thomas Schreiber, Nonlinear Time Series Analysis, Cambridge University Press, 1997.

See Also

embedSeries, determinism, timeLag.

Examples

# NOT RUN {
## 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)
# }