We provide a comprehensive analysis of the out-of-sample performance of a wide variety of spot rate models in forecasting the probability density of future interest rates. While the most parsimonious models perform best in forecasting the conditional mean of many financial time series, we find that the spot rate models that incorporate conditional heteroskedasticity and excess kurtosis or heavy-tails have better density forecasts. GARCH significantly improves the modeling of the conditional variance and kurtosis, while regime switching and jumps improve the modeling of the marginal density of interest rates. Our analysis shows that the sophisticated spot rate models in the existing literature are important for applications involving density forecasts of interest rates.

Numerous studies have shown that the simple random walk model outperforms all structural and time series models in forecasting the conditional mean of exchange rate changes. However, in many important applications, such as risk management, forecasts of the probability distribution of exchange rate changes are often needed. In this paper, we develop a nonparametric portmanteau evaluation procedure for out-of-sample density forecast and provide a comprehensive empirical study on the out-of-sample performance of a wide variety of time series models in forecasting the intraday probability density of two major exchange rates－Euro/Dollar and Yen/Dollar. We find that some nonlinear time series models provide better density forecast than the simple random walk model, although they underperform in forecasting the conditional mean. For Euro/Dollar, it is important to model heavy tails through a Student-t innovation and asymmetric time-varying conditional volatility through a regime-switching GARCH model for both in-sample and out-of-sample performance; modeling conditional mean and serial dependence in higher order moments (e.g.,conditional skewness), although important for in-sample performance, does not help out-of-sample density forecast. For Yen/Dollar, it is also important to model heavy tails and volatility clustering, and the best density forecast model is a RiskMetrics model with a Student-t innovation. As a simple application, we Þnd that the models that provide good density forecast generally provide good forecast of Value-at-Risk.