Skip to contents

Time-delay phase-space embedding

Source: R/stability-nonlinear.R
timeDelayEmbed.Rd

Reconstructs a scalar time series into a delay-embedded phase space \(Y(i) = [x_i, x_{i+\tau}, \dots, x_{i+(m-1)\tau}]\). When delay is NULL it is chosen at the first local minimum of the average mutual information (AMI); when dim is NULL it is chosen where the fraction of false nearest neighbours (FNN) first drops below fnn_threshold.

Usage

timeDelayEmbed(
  x,
  delay = NULL,
  dim = NULL,
  max_delay = 50L,
  max_dim = 10L,
  n_bins = 16L,
  fnn_threshold = 0.01
)

Arguments

x

Numeric time series.

delay

Embedding delay in samples; NULL to estimate via AMI.

dim

Embedding dimension; NULL to estimate via FNN.

max_delay

Maximum delay searched for the AMI minimum.

max_dim

Maximum embedding dimension searched for FNN.

n_bins

Histogram bins for the AMI estimate.

fnn_threshold

FNN fraction below which the dimension is accepted.

Value

A time_delay_embedding list with embedded (matrix, points x dim), delay, dim, ami (if estimated) and fnn (if estimated).

References

Fraser AM, Swinney HL (1986); Kennel MB, et al. (1992).

See also

maxLyapunovExponent(), sampleEntropy()

Examples

x <- sin(seq(0, 20 * pi, length.out = 500))
emb <- timeDelayEmbed(x, delay = 5, dim = 3)
dim(emb$embedded)
#> [1] 490   3