Makes a local linear ansatz and estimates the one step prediction error of the model. It allows to determine the optimal set of parameters for the program lfo-run, which iterates the local linear model to get a clean trajectory. The given forecast error is normalized to the variance of the data.
Input
This function always assumes that each time series is along the longer dimension of matrix S. It also assumes that every dimension (counting along the shorter dimension) of S is considered a component of the time series.
Parameters
The embedding dimension used. It is synonymous to the second part of flag ’-m’ from TISEAN. The first part of the TISEAN flag is omitted as all of the available components of S are analyzed [default = 1].
Delay used for the embedding [default = 1].
Sets for how many points the error should be calculated [default is for all of the points].
Minimum number of neighbors for the fit [default = 30].
Size of neighbourhood to start with [default = 1/1000].
Factor to increase the neighbourhood size if not enough naighbors were found [default = 1.2].
Steps to be forecast x(n+s) = f(x(n))
[default = 1].
Width of causality window [default = value of parameter ’s’].
Outputs
This is a matrix of length equal to the parameter ’s’. It contains the relative forecast error. The first column (row depending on the input) contains the steps forecasted. Relative means that the forecast error is divided by the standard deviation of the vector component. Note: This does output is different than that of lzo_test. Here it gives relative forecast error for each component globally, not for each forecasted datapoint of each component.
This is a matrix that contais the individual forecast error for each comonent of each reference point. This is the same as passing ’-V2’ to TISEAN lfo-test.
See also: lfo_ar, lfo_run.
Algorithms
The algorithms for this functions have been taken from the TISEAN package.
Package: tisean