crqa (version 1.0.6)

crqa: Cross recurrence measures of two time-series, time-delayed and embedded in higher dimensional space

Description

Core cross recurrence function, which examines recurrent structures between time-series, which are time-delayed and embedded in higher dimensional space. The approach compares the phase space trajectories of two time-series in the same phase-space when delays are introduced. A distance matrix between the two-series, delayed and embedded is calculated. Several measures representative of the interaction between two series are extracted (explained below).

Usage

crqa(ts1, ts2, delay, embed, rescale, radius, normalize,
mindiagline, minvertline, tw, whiteline, recpt, side, checkl)

Arguments

ts1

First time-series.

ts2

Second time-series.

delay

The delay unit by which the series are lagged.

embed

The number of embedding dimension for phase-reconstruction, i.e., the lag intervals.

rescale

Rescale the distance matrix; if rescale = 0 (do nothing); if rescale = 1 (mean distance of entire matrix); if rescale = 2 (maximum distance of entire matrix).

radius

A threshold, cut-off, constant used to decide whether two points are recurrent or not.

normalize

Normalize the time-series; if normalize = 0 (do nothing); if normalize = 1 (Unit interval); if normalize = 2 (z-score).

mindiagline

A minimum diagonal length of recurrent points. Usually set to 2, as it takes a minimum of two points to define any line.

minvertline

A minimum vertical length of recurrent points.

tw

The Theiler window parameter

whiteline

A logical flag to calculate (TRUE) or not (FALSE) empty vertical lines.

recpt

A logical flag indicating whether measures of cross-recurrence are calculated directly from a recurrent plot (TRUE) or not (FALSE).

side

A string indicating whether recurrence measures should be calculated in the 'upper' triangle of the RP 'lower' triangle of the matrix, or 'both'. LOC is automatically excluded for 'upper' and 'lower'.

checkl

A list with four arguments: do = TRUE|FALSE; normalize (or not) the length of ts if do == TRUE, then the arguments of checkts() needs to be passed. datatype = (numerical, categorical) - nature of ts thrshd: number of timepoints we tollerate difference between ts pad: the two series have to be padded (TRUE) or chopped (FALSE)

Value

If CRQA can be calculated and recurrence is found, it returns a list with different measures extracted from the recurrence plot. Otherwise, the values for the output arguments will be either 0 or NA.

RR

The percentage of recurrent points falling within the specified radius (range between 0 and 100)

DET

Proportion of recurrent points forming diagonal line structures.

NRLINE

The total number of lines in the recurrent plot

maxL

The length of the longest diagonal line segment in the plot, excluding the main diagonal

L

The average length of line structures

ENTR

Shannon information entropy of diagonal line lengths longer than the minimum length

rENTR

Entropy measure normalized by the number of lines observed in the plot. Handy to compare across contexts and conditions

LAM

Proportion of recurrent points forming vertical line structures

TT

The average length of vertical line structures

Details

We recommend setting whiteline = FALSE, as the current version of the library does not make use of such information to extract measures of cross-recurrence.

See Also

tt, checkts, spdiags, simts

Examples

# NOT RUN {
## simulate two dichotomous series
tS = simts(0.25, 0.05, 0.2, 0.2, 0.25, 100)
ts1 = tS[1,]; ts2 = tS[2,]

## check data(crqa) for alternative data
## (e.g., RDts1, RDts2)

## initialize the parameters

delay = 1; embed = 1; rescale = 1; radius = 0.001;
normalize = 0; mindiagline = 2; minvertline = 2;
tw = 0; whiteline = FALSE; recpt = FALSE; side = "both"
checkl = list(do = FALSE, thrshd = 3, datatype = "categorical",
    pad = TRUE)

ans = crqa(ts2, ts1, delay, embed, rescale, radius, normalize,
mindiagline, minvertline, tw, whiteline, recpt, side, checkl)

print(ans[1:9]) ## last argument of list is the cross-recurrence plot
RP = ans$RP ## take out RP

# }