Chaos01 (version 1.2.1)

rqa.seq: Function to compute diagonal RQA measures for given time series and sequence of thresholds.

Description

This function is a wrapper for the rqa function to compute RQA for a sequence of thresholds. It computes results of the RQA from the numeric vector (time series) for a sequence of thresholds given by standard parameter of the seq() function.

Usage

rqa.seq(from, to = NULL, by, TS, dim = 2, lag = 1, theta = 1,
  lmin = 3, use.by = TRUE, length.out = 100, include.TS = FALSE)

Arguments

from

double, smallest value of epsilon (threshold to be used for the computation of the rqa)

to

double, largest value of epsilon, passed to the "to" parameter of seq(). If NULL, it is set to diff(range(TS)), which is maximum possible distance in TS. Default is NULL.

by

double, increment of the sequence of threshold values, passed to the "by" parameter of seq().

TS

the input vector, This should be a numeric vector. (e.g. ts object is also accepted)

dim

integer, embedding dimension. Default is 2.

lag

integer, embedding lag/delay. Default is 1.

theta

integer, Theiler window, number of diagonal lines which should be skipped from the main diagonal.

• 0 - include main diagonal/LOS into computation

• 1 - do not include main diagonal.

• 2 - skip main diagonal and 1 diagonal closest to main diagonal.

• 3 - etc.

Default is 1.

lmin

integer, minimal length of line to be considered for recurrence line. Default is 3.

use.by

logical, indicate whether to use by statement, or length.out statement. If TRUE "by" is used. Default is TRUE.

length.out

integer, desired number of computation of rqa, passed to the "length.out" parameter of seq(). Used if "use.by = FALSE" as an alternative to creating the sequence of threshold values.

include.TS

logical, if TRUE input time series will be added to the list of outputs. Default is FALSE.

Value

Returns "chaos01.rqa.seq" object, as a list of "chaos01.rqa" objects for every "eps" given by the input parameters.

Details

RQA analysis tool is included in this package because '0-1 test for chaos' can determine whether the dynamics of the system is chaotic or regular, but cannot distinguish between chaotic and random dynamics.

It should be possible to determine whether the system is deterministic or not, based on the evolution of RQA measure with increasing thresholds 'eps'. For this it is necessary to compute RQA many times and therefore this fast version of RQA computation is provided. Function rqa.seq is wrapper for the fast.rqa function and computes RQA for a sequence of 'eps' values.

Results of this function can be easily visualized by the plot function. See plot.chaos01.rqa.sequence for more information.

Usually, RQA is computed from a state-space reconstruction of the dynamical system. In this case Takens embedding is used [3]. It is necessary to set two parameters for Takens embedding: embeding dimension and delay time. If You have no prior knowledge about the system, it is possible to estimate best values for these parameters according to the first minimal value of the mutual information of the time series and the minimal value of the false nearest neighbour algorithm. These routines can be found in e.g. 'nonlinearTseries' package and 'fNonlinear' package.

References

Marwan; M. C. Romano; M. Thiel; J. Kurths (2007). "Recurrence Plots for the Analysis of Complex Systems". Physics Reports. 438 (5-6): 237. Bibcode:2007PhR...438..237M. doi:10.1016/j.physrep.2006.11.001.

Zbilut, J.; Webber C., L. (2006). "Recurrence Quantification Analysis". Wiley Encylopedia of Biomedical Engineering, SN: 9780471740360, doi: 10.1002/9780471740360.ebs1355

See Also

fast.rqa, plot.chaos01.rqa.sequence

Examples

# NOT RUN {
vec.x <- gen.logistic(mu = 3.55, iter = 2000)

x.range <- diff(range(vec.x))

from = 0.01 * x.range
by   = 0.1 * x.range

# Output for each value of eps
res <- rqa.seq(vec.x, from = from, to = x.range, by = by, TS = vec.x, dim = 3, lag = 10)

# }
# NOT RUN {
# It is a good idea to get a grasp on how RQA develop for different colored noise.
if(requireNamespace(tuneR)){
pink  <- tuneR::noise(kind = "pink", duration = 1000)@left
red   <- tuneR::noise(kind = "red", duration = 1000)@left
power <- tuneR::noise(kind = "power", duration = 1000)@left
white <- tuneR::noise(kind = "white", duration = 1000)@left

start <- 0.001 * diff(range(TS))
end   <- 1.0   * diff(range(TS))
step  <- 0.01  * diff(range(TS))

rqa.pink  <- Chaos01::rqa.seq(start, end, step, pink, dim, lag, theta, lmin)
rqa.red   <- Chaos01::rqa.seq(start, end, step, red, dim, lag, theta, lmin)
rqa.power <- Chaos01::rqa.seq(start, end, step, power, dim, lag, theta, lmin)
rqa.white <- Chaos01::rqa.seq(start, end, step, white, dim, lag, theta, lmin)

plotvar <- c("RR", "RATIO", "DET", "LAM", "AVG", "TT", "MAX", "MAX_V")

par(mfrow = c(4,2))
plot(rqa.pink, plotvar)
plot(rqa.red, plotvar)
plot(rqa.power, plotvar)
plot(rqa.white, plotvar)
}
# }