A growing literature documents important gains in asset return volatility forecasting via use of realized variation measures constructed from high-frequency returns. We progress by using newly developed bipower variation measures and corresponding nonparametric tests for jumps. Our empirical analyses of exchange rates, equity index returns, and bond yields suggest that the volatility jump component is both highly important and distinctly less persistent than the continuous component, and that separating the rough jump moves from the smooth continuous moves results in significant out-of-sample volatility forecast improvements. Moreover, many of the significant jumps are associated with specific macroeconomic news announcements.

It depends. If volatility fluctuates in a forecastable way, volatility forecasts are useful for risk management (hence the interest in volatility forecastability in the risk management literature). Volatility forecastability, however, varies with horizon, and different horizons are relevant in different applications. Moreover, existing assessments of volatility forecastability are plagued by the fact that they are joint assessments of volatility forecastability and an assumed model, and the results can vary not only with the horizon but also with the assumed model. To address this problem, we develop a model-free procedure for assessing volatility forecastability across horizons. Perhaps surprisingly, we find that volatility forecastability decays quickly with horizon. Volatility forecastability—although clearly of relevance for risk management at the short horizons relevant for, say, trading desk management—may be much less important at longer horizons.

We provide a framework for evaluating and improving multivariate density forecasts. Among other things, the multivariate framework lets us evaluate the adequacy of density forecasts involving cross-variable interactions, such as time-varying conditional correlations. We also provide conditions under which a technique of density forecast “calibration” can be used to improve deficient density forecasts, and we show how the calibration method can be used to generate good density forecasts from econometric models, even when the conditional density is unknown. Finally, motivated by recent advances in financial risk management, we provide a detailed application to multivariate high-frequency exchange rate density forecasts.

We generalize the Franke-Härdle (1992) spectral-density bootstrap to the multivariate case. The extension is nontrivial and facilitates use of the Franke-Härdle bootstrap in frequency-domain econometric work, which often centers on crossvariable dynamic interactions. We document the bootstrap's good finite-sample performance in a small Monte Carlo experiment, and we conclude by highlighting key directions for future research.