# 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

1 2 | ```
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: |

`olag.max` |
an integer representing the maximum orbital lag
ot use in forming the results. Default: |

`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: |

`tlag` |
the delay used to create the delay embedding. Default: |

### Details

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*.

### 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 a summary of the

`spaceTime`

object.

### References

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

### See Also

`embedSeries`

, `determinism`

, `timeLag`

.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | ```
## 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)
``` |