We study the usefulness of unit root tests as diagnostic tools for selecting forecasting models. Difference stationary and trend stationary models of economic and financial time series often imply very different predictions, so deciding which model to use is tremendously important for applied...

It is well known that high-frequency asset returns are fat-tailed relative to the Gaussian distribution, and that the fat tails are typically reduced but not eliminated when returns are standardized by volatilities estimated from popular models such as GARCH. We consider two major dollar...

Market risk management traditionally has focussed on the distribution of portfolio value changes resulting from moves in the midpoint of bid and ask prices. Hence the market risk is really in a “pure” form: risk in an idealized market with no “friction” in obtaining the fair price....

We review and synthesize our recent work on realized volatility in financial markets. This includes (1) constructing and interpreting realized volatilities for a variety of asset returns ("understanding"), (2) determining underlying sampling frequencies high enough to produce precise estimates...

It depends. If volatility fluctuates in a forecastable way, then 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...

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...

Recent literature has trumpeted the claim that extreme value theory (EVT) holds promise for accurate estimation of extreme quantiles and tail probabilities of financial asset returns, and hence hold promise for advances in the management of extreme financial risks. Our view, based on a...

Using high-frequency data on Deutschemark and Yen returns against the dollar, we construct model-free estimates of daily exchange rate volatility and correlation, covering an entire decade. In addition to being model-free, our estimates are also approximately free of measurement error under...