Forcesting Foreing Exchange Rates: Bayesian Model Comparison Using Gaussian and Laplacian Noise Models

摘要

When using neural networks for forecastuing changes in foreign exchange rates, selecting a good noise model representation is improtant in obtaining both predictions and sensible error bar estimates. Making use of the Bayesian evidence framework~6, we find that the havey-tailed Laplacian moise model is better suited than the Gaussian noise model Normally, to facilitate mathematical tractability in the Bayesian evidence framework, the assumption of Gaussian residuals is often used. However, it is possible to incorporate other exponential noise models into the Bayesian framework without too much difficulty. We show that by using an alternative form of the Fisher information matrix to estimate the posterior curvature, that the Laplacian noise model can be used in the Bayesian evidence framework. Our results confirm the findings of LeBarn~4, who showed that there is large kurtosis in the distribution of price changes and non-linearity in both hourly foreign exchange data.