rqa: Recurrence Quantification Analysis (RQA)
In nonlinearTseries: Nonlinear Time Series Analysis

Description Usage Arguments Value Author(s) References Examples

The Recurrence Quantification Analysis (RQA) is an advanced technique for the nonlinear analysis that allows to quantify the number and duration of the recurrences in the phase space.

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rqa(takens = NULL, time.series = NULL, embedding.dim = 2,
  time.lag = 1, radius, lmin = 2, vmin = 2, distanceToBorder = 2,
  save.RM = TRUE, do.plot = FALSE, ...)

`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 from which the phase-space reconstruction is performed.
`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.
`radius`	Maximum distance between two phase-space points to be considered a recurrence.
`lmin`	Minimal length of a diagonal line to be considered in the RQA. Default lmin = 2.
`vmin`	Minimal length of a vertical line to be considered in the RQA. Default vmin = 2.
`distanceToBorder`	In order to avoid border effects, the distanceToBorder points near the border of the recurrence matrix are ignored when computing the RQA parameters. Default, distanceToBorder = 2.
`save.RM`	Logical value. If TRUE, the recurrence matrix is stored as a sparse matrix. Note that computing the recurrences in matrix form can be computationally expensive.
`do.plot`	Logical. If TRUE, the recurrence plot is shown. However, plotting the recurrence matrix is computationally expensive. Use with caution.
`...`	Additional plotting parameters.

A rqa object that consist of a list with the most important RQA parameters:

recurrence.matrix: A sparse symmetric matrix containing the recurrences of the phase space.
REC: Recurrence. Percentage of recurrence points in a Recurrence Plot.
DET: Determinism. Percentage of recurrence points that form diagonal lines.
LAM: Percentage of recurrent points that form vertical lines.
RATIO: Ratio between DET and RR.
Lmax: Length of the longest diagonal line.
Lmean: Mean length of the diagonal lines. The main diagonal is not taken into account.
DIV: Inverse of Lmax.
Vmax: Longest vertical line.
Vmean: Average length of the vertical lines. This parameter is also referred to as the Trapping time.
ENTR: Shannon entropy of the diagonal line lengths distribution
TREND: Trend of the number of recurrent points depending on the distance to the main diagonal
diagonalHistogram: Histogram of the length of the diagonals.
recurrenceRate: Number of recurrent points depending on the distance to the main diagonal.

Constantino A. Garcia and Gunther Sawitzki

Zbilut, J. P. and C. L. Webber. Recurrence quantification analysis. Wiley Encyclopedia of Biomedical Engineering (2006).

## Not run: 
rossler.ts =  rossler(time=seq(0, 10, by = 0.01),do.plot=FALSE)$x
rqa.analysis=rqa(time.series = rossler.ts, embedding.dim=2, time.lag=1,
               radius=1.2,lmin=2,do.plot=FALSE,distanceToBorder=2)
plot(rqa.analysis)

## End(Not run)

Loading required package: Matrix
Loading required package: rgl
Loading required package: tseries
Loading required package: TSA
Loading required package: leaps
Loading required package: locfit
locfit 1.5-9.1 	 2013-03-22
Loading required package: mgcv
Loading required package: nlme
This is mgcv 1.8-17. For overview type 'help("mgcv-package")'.

Attaching package: 'TSA'

The following objects are masked from 'package:stats':

    acf, arima

The following object is masked from 'package:utils':

    tar

Loading required package: Rcpp

Attaching package: 'nonlinearTseries'

The following object is masked from 'package:grDevices':

    contourLines

Warning messages:
1: In rgl.init(initValue, onlyNULL) : RGL: unable to open X11 display
2: 'rgl_init' failed, running with rgl.useNULL = TRUE 
3: .onUnload failed in unloadNamespace() for 'rgl', details:
  call: fun(...)
  error: object 'rgl_quit' not found