A one dimensional mapping method for time series data

The problem of constructing one dimensional map model based on time series data, especially the one dimensional map exactly reproducing the time series data is considered. A new method that employs a piecewise linear canonical representing function and implements the one dimensional map as MATLAB vectrized M-files, is proposed. The application of this method is illustrated by examples of time series data such as a Nikkei Stock Average, an exchange rate, and an EEG.