estimateEmbeddingDim {nonlinearTseries}

Estimate the embedding dimension

Description

This function determines the minimum embedding dimension from a scalar time series using the algorithm proposed by L. Cao (see references).

Usage

estimateEmbeddingDim(
  time.series,
  number.points = length(time.series),
  time.lag = 1,
  max.embedding.dim = 15,
  threshold = 0.95,
  max.relative.change = 0.1,
  do.plot = TRUE,
  main = "Computing the embedding dimension",
  xlab = "dimension (d)",
  ylab = "E1(d) & E2(d)",
  ylim = NULL,
  xlim = NULL,
  std.noise
)

Arguments

time.series

The original time series.

number.points

Number of points from the time series that will be used to estimate the embedding dimension. By default, all the points in the time series are used.

time.lag

Time lag used to build the Takens' vectors needed to estimate the embedding dimension (see buildTakens). Default: 1.

max.embedding.dim

Maximum possible embedding dimension for the time series. Default: 15.

threshold

Numerical value between 0 and 1. The embedding dimension is estimated using the E1(d) function. E1(d) stops changing when d is greater than or equal to embedding dimension, staying close to 1. This value establishes a threshold for considering that E1(d) is close to 1. Default: 0.95

max.relative.change

Maximum relative change in E1(d) with respect to E1(d-1) in order to consider that the E1 function has been stabilized and it will stop changing. Default: 0.01.

do.plot

Logical value. If TRUE (default value), a plot of E1(d) and E2(d) is shown.

main

Title for the plot.

xlab

Title for the x axis.

ylab

Title for the y axis.

ylim

numeric vectors of length 2, giving the y coordinates range.

xlim

numeric vectors of length 2, giving the x coordinates range.

std.noise

numeric value that permits to add a small amount of noise to the original series to avoid the appearance of false neighbours due to discretizacion errors. This also prevents the method to fail with periodic signals (in which neighbours at a distance of 0 appear). By default, a small amount of noise is always added. Use 0 not to add noise.

Details

The Cao's algorithm uses 2 functions in order to estimate the embedding dimension from a time series: the E1(d) and the E2(d) functions, where d denotes the dimension.

E1(d) stops changing when d is greater than or equal to the embedding dimension, staying close to 1. On the other hand, E2(d) is used to distinguish deterministic signals from stochastic signals. For deterministic signals, there exist some d such that E2(d)!=1. For stochastic signals, E2(d) is approximately 1 for all the values.

This function uses the Arya and Mount's C++ ANN library for nearest neighbour search (For more information on the ANN library please visit http://www.cs.umd.edu/~mount/ANN/). The R wrapper is a modified version of the RANN package code by Samuel E. Kemp and Gregory Jefferis.

If no suitable embedding dimension can be found within the provided range, the function will return NA.

Note

In the current version of the package, the automatic detection of stochastic signals has not been implemented yet.

Author(s)

Constantino A. Garcia

References

Cao, L. Practical method for determining the minimum embedding dimension of a scalar time series. Physica D: Nonlinear Phenomena, 110,1, pp. 43-50 (1997).

Arya S. and Mount D. M. (1993), Approximate nearest neighbor searching, Proc. 4th Ann. ACM-SIAM Symposium on Discrete Algorithms (SODA'93), 271-280.

Arya S., Mount D. M., Netanyahu N. S., Silverman R. and Wu A. Y (1998), An optimal algorithm for approximate nearest neighbor searching, Journal of the ACM, 45, 891-923.

Examples

## Not run: 
h = henon(do.plot=FALSE) 
dimension = estimateEmbeddingDim(h$x, time.lag=1, max.embedding.dim=6,
             threshold=0.9, do.plot=TRUE)
             
## End(Not run)