Using a generalized vector autoregressive framework in which forecast-error variance decompositions are invariant to variable ordering, we propose measures of both total and directional volatility spillovers. We use our methods to characterize daily volatility spillovers across U.S. stock, bond, foreign exchange and commodities markets, from January 1999 through October 2008. We show that despite significant volatility fluctuations in all markets during the sample, cross-market volatility spillovers were quite limited until the global financial crisis that began in 2007. As the crisis intensified, so too did volatility spillovers, with particularly important spillovers from the bond market to other markets. JEL classification numbers: G1, F3

We propose and evaluate explicit tests of the null hypothesis of no difference in the accuracy of two competing forecasts. In contrast to previously developed tests, a wide variety of accuracy measures can be used (in particular, the loss function need not be quadratic, and need not even be symmetric), and forecast errors can be non-Gaussian, nonzero mean, serially correlated, and contemporaneously correlated. Asymptotic and exact finite sample tests are proposed, evaluated, and illustrated.

Despite powerful advances in yield curve modeling in the last twenty years, comparatively little attention has been paid to the key practical problem of forecasting the yield curve. In this paper we do so. We use neither the no-arbitrage approach, which focuses on accurately fitting the cross section of interest rates at any given time but neglects time-series dynamics, nor the equilibrium approach, which focuses on time-series dynamics (primarily those of the instantaneous rate) but pays comparatively little attention to fitting the entire cross section at any given time and has been shown to forecast poorly. Instead, we use variations on the Nelson-Siegel exponential components framework to model the entire yield curve, period-by-period, as a three-dimensional parameter evolving dynamically. We show that the three time-varying parameters may be interpreted as factors corresponding to level, slope and curvature, and that they may be estimated with high efficiency. We propose and estimate autoregressive models for the factors, and we show that our models are consistent with a variety of stylized facts regarding the yield curve. We use our models to produce term-structure forecasts at both short and long horizons, with encouraging results. In particular, our forecasts appear much more accurate at long horizons than various standard benchmark forecasts. JEL Codes: G1, E4, C5Key Words: Term structure, yield curve, factor model, Nelson-Siegel curve Acknowledgments: The National Science Foundation, the Wharton Financial Institutions Center, and the Guggenheim Foundation provided research support. For helpful comments we are grateful to the Editor (Arnold Zellner), the Associate Editor, and three referees, as well as Dave Backus, Rob Bliss, Michael Brandt, Todd Clark, Qiang Dai, Ron Gallant, Mike Gibbons, David Marshall, Monika Piazzesi, Eric Renault, Glenn Rudebusch, Til Schuermann, and Stan Zin, and seminar participants at Geneva, Georgetown, Wharton, the European Central Bank, and the National Bureau of Economic Research. We, however, bear full responsibility for all remaining flaws. 1 The empirical literature that models yields as a cointegrated system, typically with one underlying stochastic trend (the short rate) and stationary spreads relative to the short rate, is similar in