Forecasting Exchange Rates: A Chaos-Based Regression Approach

Abstract

Accurate forecasting for future events constitutes a fascinating challenge for theoretical and for applied researches. Foreign Exchange market FOREX is selected in this research to represent an example of financial systems with a complex behavior. Forecasting a financial time series can be a very hard task due to the inherent uncertainty nature of these systems. It seems very difficult to tell whether a series is stochastic or deterministic chaotic or some combination of these states. More generally, the extent to which a non-linear deterministic process retains its properties when corrupted by noise is also unclear. The noise can affect a system in different ways even though the equations of the system remain deterministic. Since a single reliable statistical test for chaoticity is not available, combining multiple tests is a crucial aspect, especially when one is dealing with limited and noisy data sets like in economic and financial time series. In this research, the authors propose an improved model for forecasting exchange rates based on chaos theory that involves phase space reconstruction from the observed time series and the use of support vector regression SVR for forecasting.Given the exchange rates of a currency pair as scalar observations, observed time series is first analyzed to verify the existence of underlying nonlinear dynamics governing its evolution over time. Then, the time series is embedded into a higher dimensional phase space using embedding parameters.In the selection process to find the optimal embedding parameters,a novel method based on the Differential Evolution DE geneticalgorithmas a global optimization technique was applied. The authors have compared forecasting accuracy of the proposed model against the ordinary use of support vector regression. The experimental results demonstrate that the proposed method, which is based on chaos theory and genetic algorithm,is comparable with the existing approaches.