Estimation of the proper embedding dimension for a single-variable time series

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Description

Invokes the method of False Nearest Neighbors (FNN) to estimate the minimal embedding dimension of a multivariate data set.

Usage

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FNN(x, dimension=5, tlag=NULL, rtol=10, atol=2, olag=1)

Arguments

x

a vector containing a uniformly-sampled real-valued time series.

atol

neighbor tolerance based on attractor size. If the Euclidean distance between two neighbor candidates is Atol times larger the estimated "size" of the attractor, then those neighbors are declared as false neighbors. Default: 2.

dimension

the maximal embedding dimension. Default: 5.

olag

orbital lag. The number of points along the trajectory (orbit) of the current point that must be exceeded in order for another point in the phase space to be considered a neighbor candidate. This argument is used to help attenuate temporal correlation in the the embedding which can lead to spuriously low minimal embedding dimension estimates. The orbital lag must be positive or zero. Default: 0.

rtol

false neighbor Euclidean distance tolerance. If the ratio of the Euclidean distances between neighbor candidates in successive embedding dimensions exceeds Rtol, then those neighbors are declared as false neighbors. For example, if Rtol=5 neighbor candidates that are separated five times more so than in the previous embedding dimension are declared false neighbors. Default: 10.

tlag

the time delay between coordinates. Default: the decorrelation time of the autocorrelation function.

Value

an object of class FNN.

S3 METHODS

plot

plots a summary of the results. Available options are:

xlab

a character string defining the x-axis label. Default: "Embedding Dimension".

ylab

a character string defining the y-axis label. Default: "FNN percentage".

...

Additional plot arguments (set internally by the par function).

print

prints a summary of the results. Available options are:

...

Additional print arguments used by the standard print function.

References

M. B. Kennel, R. Brown, and H. D. I. Abarbanel (1992), Determining embedding dimension for phase-space reconstruction using a geometrical construction, Physical Review A, 45(6), 3403–3411.

Fredkin, D. R., and Rice, J. A. (1995), Method of false nearest neighbors: A cautionary note, Physical Review E, 51(4), 2950–2954.

See Also

FNS, embedSeries, infoDim, corrDim, timeLag, determinism.

Examples

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## perform False Nearest Neighbors tests on 
## chaotic beam data for embedding dimensions 1 
## through 10, using a time delay embedding 
## with a time lag of 10 and an orbital lag of 
## 15 
x <- FNN(beamchaos, tlag=10, olag=15 )

## print the results 
print(x)

## plot the results 
plot(x)

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