Simplex: Simplex forecasting

In rEDM: Empirical Dynamic Modeling ('EDM')

Simplex forecasting

Description

Simplex performs time series forecasting based on weighted nearest neighbors projection in the time series phase space as described in Sugihara and May.

Usage

Simplex(pathIn = "./", dataFile = "", dataFrame = NULL, pathOut = "./", 
  predictFile = "", lib = "", pred = "", E = 0, Tp = 1, knn = 0, tau = -1, 
  exclusionRadius = 0, columns = "", target = "", embedded = FALSE,
  verbose = FALSE, validLib = vector(), generateSteps = 0,
  parameterList = FALSE, showPlot = FALSE, noTime = FALSE)

Arguments

pathIn	path to dataFile.
dataFile	.csv format data file name. The first column must be a time index or time values unless noTime is TRUE. The first row must be column names.
dataFrame	input data.frame. The first column must be a time index or time values unless noTime is TRUE. The columns must be named.
pathOut	path for predictFile containing output predictions.
predictFile	output file name.
lib	string or vector with start and stop indices of input data rows used to create the library from observations. Mulitple row index pairs can be specified with each pair defining the first and last rows of time series observation segments used to create the library.
pred	string with start and stop indices of input data rows used for predictions. A single contiguous range is supported.
E	embedding dimension.
Tp	prediction horizon (number of time column rows).
knn	number of nearest neighbors. If knn=0, knn is set to E+1.
tau	lag of time delay embedding specified as number of time column rows.
exclusionRadius	excludes vectors from the search space of nearest neighbors if their relative time index is within exclusionRadius.
columns	string of whitespace separated column name(s) in the input data used to create the library.
target	column name in the input data used for prediction.
embedded	logical specifying if the input data are embedded.
verbose	logical to produce additional console reporting.
validLib	logical vector the same length as the number of data rows. Any data row represented in this vector as FALSE, will not be included in the library.
generateSteps	number of predictive feedback generative steps.
parameterList	logical to add list of invoked parameters.
showPlot	logical to plot results.
noTime	logical to allow input data with no time column.

Details

If embedded is FALSE, the data column(s) are embedded to dimension E with time lag tau. This embedding forms an E-dimensional phase space for the Simplex projection. If embedded is TRUE, the data are assumed to contain an E-dimensional embedding with E equal to the number of columns. Predictions are made using leave-one-out cross-validation, i.e. observation vectors are excluded from the prediction simplex.

To assess an optimal embedding dimension EmbedDimension can be applied. Accuracy statistics can be estimated by ComputeError.

Value

A data.frame with columns Observations, Predictions. The first column contains the time values.

If parameterList = TRUE, a named list with "predictions" holding the data.frame, "parameters" with a named list of invoked parameters.

References

Sugihara G. and May R. 1990. Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature, 344:734-741.

Examples

data( block_3sp )
smplx = Simplex( dataFrame = block_3sp, lib = "1 100", pred = "101 190",
E = 3, columns = "x_t", target = "x_t" )
ComputeError( smplx $ Predictions, smplx $ Observations )

rEDM documentation built on Nov. 10, 2023, 5:08 p.m.