spaceTimePlot {nonlinearTseries}

Space Time plot

Description

The space time separation is a broadly-used method of detecting non-stationarity and temporal correlations in the time series being analyzed. The space time separation plot is also used to select a proper Theiler window by selecting a temporal separation enough to saturate the contour lines.

Usage

spaceTimePlot(
  takens = NULL,
  time.series = NULL,
  embedding.dim = 2,
  time.lag = 1,
  max.radius = NULL,
  time.step = 1,
  number.time.steps = NULL,
  numberPercentages = 10,
  do.plot = TRUE,
  ...
)

## S3 method for class 'spaceTimePlot'
contourLines(x)

## S3 method for class 'spaceTimePlot'
getContourLines(x)

## S3 method for class 'spaceTimePlot'
plot(
  x,
  main = "Space time separation plot",
  xlab = NULL,
  ylab = NULL,
  type = "l",
  ylim = NULL,
  col = NULL,
  pch = NULL,
  add.legend = TRUE,
  ...
)

Arguments

takens

Instead of specifying the time.series, the embedding.dim and the time.lag, the user may specify directly the Takens' vectors.

time.series

The original time series being analyzed.

embedding.dim

Integer denoting the dimension in which we shall embed the time series.

time.lag

Integer denoting the number of time steps that will be use to construct the Takens' vectors.

max.radius

Maximum neighbourhood radius in which the algorithm will look for finding neighbours. This parameter may be used to avoid heavy computations. If the user does not specify a radius, the algorithm estimates it.

time.step

Integer denoting the number of discrete steps between two calculations of the space time plot.

number.time.steps

Integer denoting the number of temporal jumps in steps of time.step in which we want to compute the space time plot.

numberPercentages

Number of contour lines to be computed. Each contour line represent a concrete percentage of points (see Details).

do.plot

Logical. If TRUE, the time space plot is shown.

...

Additional plotting parameters.

x

A spaceTimePlot object.

main

A title for the plot.

xlab

A title for the x axis.

ylab

A title for the y axis.

type

Type of plot (see ?plot).

ylim

Numeric vector of length 2, giving the y coordinates range.

col

Vector of colors for each of the percentages of the plot.

pch

Vector of symbols for each of the percentages of the plot.

add.legend

add a legend to the plot?

Details

Each contour line of the space time plot indicate the distance you have to go (y-axis) to find a given fraction of neighbour pairs, depending on their temporal separation (x-axis).

WARNING: The parameter number.time.steps should be used with caution since this method performs heavy computations.

Value

A timeSpacePlot object that consist, essentially, of a matrix storing the values for each contour line. Each row stores the value for a given percentage of points. Each column stores the value of the radius you have to go to find a given fraction of neighbour pairs (the rows), depending on their temporal separation (the colums). This matrix can be accessed by using the contourlines method.

The contourLines function returns the contour lines of the space time plot.

Author(s)

Constantino A. Garcia

References

H. Kantz and T. Schreiber: Nonlinear Time series Analysis (Cambridge university press)

Examples

 ## Not run: 
 tak = buildTakens(sin(2*pi*0.005*(0:5000)),2,1)
 stp.test = spaceTimePlot(takens=tak,number.time.steps=400,do.plot=TRUE)
 
## End(Not run)