rEDM (version 1.14.3)

Simplex: 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,
  const_pred = FALSE, verbose = FALSE, validLib = vector(),
  generateSteps = 0, parameterList = FALSE, showPlot = FALSE)

Value

A data.frame with columns Observations, Predictions. If const_pred is TRUE the column Const_Predictions is added. 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.

Arguments

pathIn

path to dataFile.

dataFile

.csv format data file name. The first column must be a time index or time values. The first row must be column names.

dataFrame

input data.frame. The first column must be a time index or time values. The columns must be named.

pathOut

path for predictFile containing output predictions.

predictFile

output file name.

lib

string with start and stop indices of input data rows used to create the library of observations. A single contiguous range is supported.

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.

const_pred

logical to add a constant predictor column to the output. The constant predictor is X(t+1) = X(t).

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.

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.

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 )