Several authors have recently investigated the predictability of exchange rates by fitting a sequence of long-horizon error-correction equations. We show by means of a simulation study that, in small to medium samples, inference from this regression procedure depends on the null hypothesis that is used to generate empirical critical values. The standard assumption of a stationary error-correction term between exchange rates and fundamentals biases the results in favor of predictive power. Our results show that evidence of long-horizon predictability weakens when using empirical critical values generated under the more stringent null of no cointegration. Likewise, results are weakened using critical values generated under the null that exchange rates and fundamentals are generated by an unrestricted VAR with no integration restrictions.

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.

ABSTRACT In recent years, the trading accounts at large commercial banks have grown substantially and become progressively more diverse and complex. We provide descriptive statistics on the trading revenues from such activities and on the associated Value‐at‐Risk (VaR) forecasts internally estimated by banks. For a sample of large bank holding companies, we evaluate the performance of banks trading risk models by examining the statistical accuracy of the VaR forecasts. Although a substantial literature has examined the statistical and economic meaning of Value‐at‐Risk models, this article is the first to provide a detailed analysis of the performance of models actually in use.

We propose a constructive, multivariate framework for assessing agreement between (generally misspecified) dynamic equilibrium models and data, which enables a complete second-order comparison of the dynamic properties of models and data. We use bootstrap algorithms to evaluate the significance of deviations between models and data, and we use goodness-of-fit criteria to produce estimators that optimize economically-relevant loss functions. We provide a detailed illustrative application to modelling the U.S. cattle cycle.