R/nonLinearPrediction.R

In nonlinearTseries: Nonlinear Time Series Analysis

# References: http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.1/docs/chaospaper/node23.html#SECTION00061000000000000000
#' Nonlinear time series prediction
#' @description
#' Function for predicting futures values of a given time series using previous 
#' values and  nonlinear analysis techniques. 
#' @details
#' Using \emph{time.series} measurements, an embedding in 
#' \emph{embedding.dim}-dimensional phase space with time lag \emph{time.lag} 
#' is used to predict the value following the given time series after 
#' \emph{prediction.steps} sample steps. This is done by finding all the 
#' neighbours of the last Takens' vector in a  radius of size \emph{radius}  
#' (the max norm is used). If no neighbours are found within a distance radius, 
#' the neighbourhood size is increased until succesful using 
#' \emph{radius.increment}(\emph{radius} = \emph{radius} + 
#' \emph{radius.increment}).
#' @param time.series Previous values of the time series that the algorithm 
#' will use to make the prediction.
#' @param embedding.dim Integer denoting the dimension in which we shall embed 
#' the \emph{time.series}.
#' @param time.lag Integer denoting the number of time steps that will be use 
#' to construct the  Takens' vectors.
#' @param radius The radius used to looking for neighbours in the phase space 
#' (see details).
#' @param radius.increment The increment used when no neighbours are found 
#' (see details).
#' @param prediction.step Integer denoting the number of time steps ahead for 
#' the forecasting.
#' @return The predicted value \emph{prediction.step} time steps ahead.
#' @references H. Kantz  and T. Schreiber: Nonlinear Time series Analysis 
#' (Cambridge university press)
#' @examples
#' \dontrun{
#' h=henon(n.sample=5000,start=c(0.324,-0.8233))
#' predic=nonLinearPrediction(time.series=h$x[10:2000],embedding.dim=2,
#'                            time.lag=1,
#'                            prediction.step=3,radius=0.03,
#'                            radius.increment=0.03/2)
#' cat("real value: ",h$x[2003],"Vs Forecast:",predic)
#' }
#' @author Constantino A. Garcia
#' @rdname nonLinearPrediction
#' @export nonLinearPrediction
nonLinearPrediction = function(time.series, embedding.dim, time.lag, 
                               prediction.step, radius, radius.increment) {
  nfound = 0
  av = 0
  l = length(time.series)
  #vector of lag delays used to build the takens' vectors
  jumpsvect = seq((embedding.dim - 1) * time.lag, 0, -time.lag)
  # reference takensVector
  takensVector = time.series[l - jumpsvect]
  # first position that we can use for construct a 'reverse' takens' vector:
  # t(n)=[t(n-(m-1)*time.lag),t(n-(m-2)*time.lag),...,t(n)]
  beg = (embedding.dim - 1) * time.lag + 1
  # last position having into account that we want to use it to predict 
  # prediction.steps steps forward
  en = l - prediction.step
  # while  no neighbours are found, we increase the size of the neighbourhood
  while (nfound == 0) {
    # build takens vectors and check if there exist some neighbour
    for (i in beg:en) {
      if (isNeighbour(takensVector, time.series[i - jumpsvect],
                      embedding.dim, radius)) {
        #average of predictions
        av = av + time.series[[i + prediction.step]]
        nfound = nfound + 1
      }
    }
    #increment the size of the neighbourhood
    radius = radius + radius.increment   
  }
  av / nfound
}