Last data update: 2014.03.03

R: Estimate the embedding dimension
estimateEmbeddingDimR Documentation

Estimate the embedding dimension


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


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)



The original time series.


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


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


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


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.


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


Title for the plot.


Title for the x axis.


Title for the y axis.


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


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


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 The R wrapper is a modified version of the RANN package code by Samuel E. Kemp and Gregory Jefferis.


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


Constantino A. Garcia


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.


## 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)