Wavelet-based relevance vector regression model coupled with phase space reconstruction for exchange rate forecasting

Due to the high risk associated with international transactions, exchange rate forecasting is a challenging and important field in modern time series analysis. The difficulty in forecasting arises from the nonlinearity and non-stationarity inherent in exchange rate dynamics. To address these problems, this study proposes a hybrid model that couples two effective feature extraction techniques, phase space reconstruction, and wavelet analysis, with a Relevance Vector Regression (RVR) model to forecast chaotic exchange rates. The time series inputs are first mapped into high-dimension phase space, and then the phase space signal is decomposed on a wavelet basis to analyze its dynamics under various frequencies. Finally, each wavelet component is fed into a local RVR to perform non-parametric regression and forecasting. Compared with other forecasting models, such as support vector machines (SVR), RVR, GJR-GARCH or pure wavelet-base models, the proposed model performs best and statistically improves forecasting performance under root mean square error (RMSE), mean absolute error (MAE) and directional symmetry (DS).