Rainer Hegger Holger Kantz Thomas Schreiber
Exercise 2 using TISEAN Nonlinear Time Series Routines

Exercises using TISEAN
Part II: Linear models and simple prediction

Download the data set amplitude.dat to your local directory for use in this exercise (Press the "Shift"-key and the left mouse button).

Visual analysis of data, time scales, and correlations
Embedding and time lags

Determinism and predictability

You should be able to verify the following observations:
For increasing prediction horizion, the prediction errors of amplitude.dat show two regimes: Exponential increase of the error due to chaos (the regime of nonlinear deterministic dynamics), slow linear increase due to loss of phase locking (the regime of linear correlations due to the rather constant period of the oscillations), constant when the predictions lose all correlations to the actual values (limit of unpredictability for a large prediction horizon of more time steps than can be computed with this data set, the relative prediction error saturates at 1. In order to arrive a prediction horizons larger than one half of the data set, you must switch off the causality window by the -C0 option in zeroth).

No succesful prediction for ar.dat beyond the linear correlations. Since ar.dat is a linear stochastic data set, it does not contain phase space information.