# phaseSpaceReconstruction

Convert observed time series to state vectors

## Syntax

## Description

returns the reconstructed phase space `XR`

= phaseSpaceReconstruction(`X`

,`lag`

,`dim`

)`XR`

of the uniformly
sampled time-domain signal `X`

with time delay
`lag`

and embedding dimension `dim`

as
inputs.

Use `phaseSpaceReconstruction`

to verify the system order and
reconstruct all dynamic system variables, while preserving system properties.
Reconstructing the phase space is useful when limited data is available, or when
the phase space dimension and lag is unknown. The nonlinear features `approximateEntropy`

, `correlationDimension`

, and `lyapunovExponent`

use `phaseSpaceReconstruction`

as the first step of the computation.

`[___] = phaseSpaceReconstruction(___,`

returns the reconstructed phase space `Name,Value`

)`XR`

with additional
options specified by one or more `Name,Value`

pair
arguments.

`phaseSpaceReconstruction(___)`

with no output
arguments creates a matrix of sub-axes of the reconstructed phase space with
histogram plots along the diagonal.

## Examples

## Input Arguments

## Output Arguments

## Algorithms

## References

[1] Rhodes, Carl & Morari,
Manfred. "False Nearest Neighbors Algorithm and Noise Corrupted Time Series."
*Physical Review. E*. 55.10.1103/PhysRevE.55.6162.

[2] Kliková, B., and Aleš Raidl.
"Reconstruction of phase space of dynamical systems using method of time delay."
*Proceedings of the 20th Annual Conference of Doctoral Students*
WDS 2011.

[3] I. Vlachos, D. Kugiumtzis,
"State Space Reconstruction for Multivariate Time Series Prediction", *Nonlinear Phenomena in Complex Systems*, Vol 11, No 2, pp
241-249, 2008.

[4] Kantz, H., and Schreiber, T.
*Nonlinear Time Series Analysis*. Cambridge:
Cambridge University Press, Vol. 7, 2004.

## Extended Capabilities

## Version History

**Introduced in R2018a**

## See Also

`approximateEntropy`

| `lyapunovExponent`

| `correlationDimension`