ON THE PREDICTION OF THE EXCHANGE RATE USD/EURO BY CHAOS THEORY

摘要

Chaos is, by its nature, determinist. The possibility of short-term prediction of chaotic time series is the main feature that distinguishes the chaotic time series from random time series. Using chaos theory for prediction involves the reconstruction of phase space and prediction in phase space and then reconstruction of the original time series. One simple prediction procedure is the first-order approximation. If we want to predict the value x_(t+1)~d when the previous values are known, first we find the closest neighbors x_(s_i)~d of x_t~d and we consider that the values x_(s_i+1)~d are predictions for x_(t+1)~d. To obtain better predictions we can take an average of predictions obtained with the k nearest neighbors of x_t~d. In order to predict a chaotic system we need a number of observations for time series long enough to produce a sequence of vectors in phase space that cover quite well the attractor. The new values will be very close to those already observed. In this paper we will consider the exchange rate USD/EURO, underline their chaotic behavior and we will make predictions using k nearest trajectories algorithm.