# buildTakens: Build the Takens' vectors In nonlinearTseries: Nonlinear Time Series Analysis

## 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

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

## 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.

## 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).

## Author(s)

Constantino A. Garcia and Gunther Sawitzki.

## References

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

## Examples

 ```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) ```

### Example output

```Attaching package: 'nonlinearTseries'

The following object is masked from 'package:grDevices':

contourLines

Warning messages:
1: In rgl.init(initValue, onlyNULL) : RGL: unable to open X11 display
2: 'rgl_init' failed, running with rgl.useNULL = TRUE