Description Usage Arguments Value Author(s) References Examples
This function builds the Takens' vectors from a given time series. The set of Takens' vector 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.
1 | buildTakens(time.series, embedding.dim, time.lag)
|
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. |
A matrix containing the Takens' vectors (one per row).
Constantino A. Garcia
H. Kantz and T. Schreiber: Nonlinear Time series Analysis (Cambridge university press)
1 2 3 4 5 6 7 8 9 | ## Not run:
# 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)
## End(Not run)
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