embedding

0th

Percentile

Construction of embedding vectors using the method of delays

This function generates both the uniform and non-uniform embedding vectors set from an univariate time serie considering the argument set selected by the user.

Usage
embedding(x, m = 3, lag = 1, timelapse = c("FIXED", "VARIABLE"))
Arguments
x

a numeric vector, time serie, data frame or matrix depending on the method selected in timelapse.

m

a non-negative integer denoting the embedding dimension (Default 3).

lag

a non-negative integer denoting the reconstruction delay (Default 1).

timelapse

a character denoting if you consider that the observations are sampled at uniform time intervals FIXED or with a variable time-lapse between each observation VARIABLE (Default FIXED).

Details

If FIXED has been selected x must be a numeric vector or time serie. Otherwise VARIABLE has to be specified. In this case x must be a data frame or matrix with two columns. First, the date with the following format YMD H:M:OS3 considering milliseconds e.g., 20190407 00:00:03.347. If you don't consider milliseconds you must put .000 after the seconds. It should be an object of class Factor. Second, the univariate time serie as a sequence of numerical values.

Value

A data frame with the uniform or non-uniform embedding vectors by columns from an univariate time serie considering the parameter set selected by the user.

References

Ruelle, D., Takens, F. 1971 On the nature of turbulence. Communications in Mathematical Physics 20(3):167-192.

Packard, N.H., Crutchfield, J.P., Farmer, J.D., Shaw, R.S. 1980 Geometry from a time serie. Physical Review Letters 45:712-716.

Takens, F. 1981 Detecting strange attractors in turbulence. Springer Berlin Heidelberg.

Sauer, T., Yorke, J.A., Casdagli, M. 1991 Embedology. Journal of Statistical Physics 65(3):579-616.

Huke, J.P., Broomhead, D.S. 2007 Embedding theorems for non-uniformly sampled dynamical systems. Nonlinearity 20(9):205-244.

See Also

jacobi

Aliases
  • embedding
Examples
# NOT RUN {
## The first ten values corresponding to the uniform embedding
## vectors set for m=5 and lag=1 are showed by simulating
## time series from the logistic equation.
data<-logistic.ts(u.min=4,u.max=4,B=100,doplot=FALSE)
ts<-data$`Logistic 100`$time.serie
embed<-embedding(ts,m=5,lag=1,timelapse="FIXED")
show(head(embed, 10))
# }
Documentation reproduced from package DChaos, version 0.1-1, License: GPL (>= 2)

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