Student-t Mixture Density Networks for Multivariate Exchange Rate Density Forecasting: Evidence from Ghana
This study proposes a Student-t Mixture Density Network (St-MDN) for multivariate probabilistic density forecasting of Ghana Cedi exchange rates against the US Dollar, British Pound, and Euro. Using 222 monthly observations spanning January 2005 to June 2025, we demonstrate that the monthly log-returns of all three currency pairs exhibit severe leptokurtosis (excess kurtosis 9.55–14.65) and significant negative skewness, rendering the standard Gaussian assumption untenable. The St-MDN maps eleven macroeconomic covariates, including inflation, money supply (M2), interest rates, and commodity prices through a two-hidden-layer feedforward network to the parameters of a K-component mixture of Student-t distributions, jointly estimating location, scale, and degrees-of-freedom parameters for each component. Maximum likelihood estimation under the Student-t mixture likelihood yields AIC improvements of 101.7–284.8 units over the Gaussian benchmark. Out-of-sample evaluation confirms that the St-MDN delivers superior probabilistic calibration, with CRPS reductions of 28–39% relative to Gaussian mixture networks, and empirical 90% prediction interval coverage of 90.8–91.4%, near the nominal level. Feature importance analysis identifies M2 growth, the interest rate differential, and inflation as the dominant drivers of exchange rate dynamics. These findings establish the St-MDN as a principled and practically superior framework for exchange rate density forecasting in emerging market economies characterized by heavy-tailed financial data.
