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.

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.

Does the termination probability of a business expansion or contraction increase with age? This question may be formally addressed by analyzing the nature of duration dependence in aggregate economic activity. Our null hypothesis is that there is no duration dependence, which we test via intentionally nonparametric procedures. We also argue that common notion of business cycle periodicity can be usefully interpreted in terms of whole-cycle duration dependence. We find some evidence for duration dependence in whole cycles and in prewar expansions, but little evidence elsewhere.

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.

Richard T. Baillie and Tim Bollerslev (1989) have recently argued that nominal dollar spot exchange rates are cointegrated. Here the authors examine an immediate implication of their finding, namely, that cointegration implies an error-correction representation yielding forecasts superior to those from a martingale benchmark in light of a large earlier literature highlighting the predictive superiority of the martingale. In an out-of-sample forecasting exercise, the authors find the martingale model to be superior. They then perform a battery of improved cointegration tests and find that the evidence for cointegration is much less strong than previously thought, a result consistent with the outcome of the forecasting exercise.

Baillie and Bollerslev (1989) have recently argued that nominal dollar spot exchange rates are cointegrated. Here we examine an immediate implication of their finding, namely, that cointegration implies an error‐correction representation yielding forecasts superior to those from a martingale benchmark, in light of a large earlier literature highlighting the predictive superiority of the martingale. In an out‐of‐sample forecasting exercise, we find the martingale model to be superior. We then perform a battery of improved cointegration tests and find that the evidence for cointegration is much less strong than previously thought, a result consistent with the outcome of the forecasting exercise.

Purchasing power parity is one of the most important equilibrium conditions in international macroeconomics. Empirically, it is also one of the most hotly contested. Numerous recent studies, for example, have sought to determine the validity of purchasing power parity using data from the post-Bretton Woods float and have reached different conclusions. We assert that most such studies are flawed for two reasons. First, the post-1973 data contain, by definition, only a very limited amount of the low-frequency information relevant for examination of long-run parity. Second, the dynamic econometric techniques used to model deviations from parity are typically quite crude with respect to admissible low-frequency dynamics. Both deficiencies are rectified in the present paper, with dramatic results. We construct a new data set of 16 real exchange rates covering more than a century of the classic gold standard period, and we study deviations from parity using long-memory models that allow for subtle forms of mean reversion. For each real exchange rate, we find that purchasing power parity holds in the long run.

Purchasing power parity is one of the most important equilibrium conditions in international macroeconomics. Empirically, it is also one of the most hotly contested. Numerous recent studies, for example, have sought to determine the validity of purchasing power parity using data from the post-Bretton Woods float and have reached different conclusions. We assert that most such studies are flawed for two reasons. First, the post-1973 data contain, by definition, only a very limited amount of the low-frequency information relevant for examination of long-run parity. Second, the dynamic econometric techniques used to model deviations from parity are typically quite crude with respect to admissible low-frequency dynamics. Both deficiencies are rectified in the present paper, with dramatic results. We construct a new data set of 16 real exchange rates covering more than a century of the classic gold standard period, and we study deviations from parity using long-memory models that allow for subtle forms of mean reversion. For each real exchange rate, we find that purchasing power parity holds in the long run.