optimise_embedding_dim: Finds the optimal embedding dimensions and embedding lags for...

In kahaaga/tstools: Useful functions

Description

The function works by first finding the minimal embedding dimension E by either the false nearest neighbours (FNN) method, or by Whitney's embedding theorem (the minimum embedding dimension must be at least the first integer dimension larger than the box counting dimension of the attractor). The minimal embedding dimension found is then used as input for the simplex projection algorithm, which estimates a suitable E by optimizing self-prediciton.

Usage

optimise_embedding_dim(v, optimise.simplex = T, optimise.FNNdim = T,
  optimise.boxcountdim = T, min.embedding.dim = 2, max.embedding.dim = 10,
  orbital.lag = NULL, lag.max = ceiling(length(v) * 0.2),
  lag.method = "mi", embedding.lag = 1, plot.simplex.projection = F,
  return.all = T)

Arguments

v	Numeric vector containing the series.
optimise.simplex	Optimise using simplex projection?
optimise.FNNdim	Should false nearest neighbour criteria be applied?
optimise.boxcountdim	Should box counting dimension criteria be applied?
min.embedding.dim	The minimum embedding dimension to consider.
max.embedding.dim	The maximum embedding dimension to consider.
orbital.lag	The Theiler window. An orbital lag to avoid temporal correlation. Defaults to NULL, in which case the orbital lag is chosen as the first local minima of the autocorrelation function (lag.method = "acf" or lag.method = "autocorrelationfunction") or the lagged mutual information function (lag.method = "mi" or lag.method = "mutual information").
lag.max	The maximum number of lags for the autocorrelation function (lag.method = "acf" or lag.method = "autocorrelation function") or the mutual information function (lag.method = "mi" or lag.method = "mutual information function").
lag.method	The method to compute the orbital lag (Theiler window), which excludes temporal neighbours to reduce correlation bias. Either use the autocorrelation function (lag.method = "acf" or "autocorrelation") or the lagged mutual information function (lag.method = "mi" or "mutual information").
embedding.lag	The embedding lag.
plot.simplex.projection	Plot the results of the simplex projection?
return.all	Should all optimisation results be returned? Defaults to TRUE.

Details

Both pre-estimation methods may be used simultaneously. In this case, the minimal embedding dimension is the maximum of the FNN and the boxcount estimates. The final embedding dimension is then determined by simplex projection over dimensions E:max.E.

If no optimization is done prior to simplex projection, optimization is performed over dimensions min.E:max.E. min.E defaults to 2.

The embedding lag is estimated from the simplex projection routine.

Value

A data frame containing the optimal embeddings.

kahaaga/tstools documentation built on May 24, 2019, 5:01 a.m.