nonlinearTseries (version 0.3.1)

buildTakens: Build the Takens' vectors

Description

This function builds the Takens' vectors from a given time series. The set of Takens' vectors is the result of embedding the time series in a m-dimensional space. That is, the \(n^{th}\) Takens' vector is defined as $$T[n]=\{time.series[n], time.series[n+ timeLag],...time.series[n+m*timeLag]\}.$$ Taken's theorem states that we can then reconstruct an equivalent dynamical system to the original one (the dynamical system that generated the observed time series) by using the Takens' vectors.

Usage

buildTakens(time.series, embedding.dim, time.lag)

Value

A matrix containing the Takens' vectors (one per row). The resulting matrix also contains information about the time lag and the embedding dimension used (as attributes).

Arguments

time.series

The original time series.

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.

Author

Constantino A. Garcia and Gunther Sawitzki.

References

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

Examples

if (FALSE) {
# Build the Takens vector for the Henon map using the x-coordinate time series
h = henon(n.sample=  3000,n.transient= 100, a = 1.4, b = 0.3, 
start = c(0.73954883, 0.04772637), do.plot = FALSE)
takens = buildTakens(h$x,embedding.dim=2,time.lag=1)
# using the x-coordinate time series we are able to reconstruct
# the state space of the Henon map
plot(takens)}