this paper is built. First, although raw returns are clearly leptokurtic, returns standardized by realized volatilities are approximately Gaussian. Second, although the distributions of realized volatilities are clearly right-skewed, the distributions of the logarithms of realized volatilities are approximately Gaussian. Third, the long-run dynamics of realized logarithmic volatilities are well approximated by a fractionally-integrated long-memory process. Motivated by the three ABDL empirical regularities, we proceed to estimate and evaluate a multivariate model for the logarithmic realized volatilities: a fractionally-integrated Gaussian vector autoregression (VAR) . Importantly, our approach explicitly permits measurement errors in the realized volatilities. Comparing the resulting volatility forecasts to those obtained from currently popular daily volatility models and more complicated high-frequency models, we find that our simple Gaussian VAR forecasts generally produce superior forecasts. Furthermore, we show that, given the theoretically motivated and empirically plausible assumption of normally distributed returns conditional on the realized volatilities, the resulting lognormal-normal mixture forecast distribution provides conditionally well-calibrated density forecasts of returns, from which we obtain accurate estimates of conditional return quantiles. In the remainder of this paper, we proceed as follows. We begin in section 2 by formally developing the relevant quadratic variation theory within a standard frictionless arbitrage-free multivariate pricing environment. In section 3 we discuss the practical construction of realized volatilities from high-frequency foreign exchange returns. Next, in section 4 we summarize the salient distributional features of r...

It is obvious that forecasts are of great importance and widely used in economics and finance. Quite simply, good forecasts lead to good decisions. The importance of forecast evaluation and combination techniques follows immediately-- forecast users naturally have a keen interest in monitoring and improving forecast performance. More generally, forecast evaluation figures prominently in many questions in empirical economics and finance, such as: Are expectations rational? (e.g., Keane and Runkle, 1990; Bonham and Cohen, 1995) Are financial markets efficient? (e.g., Fama, 1970, 1991) Do macroeconomic shocks cause agents to revise their forecasts at all horizons, or just at short- and medium-term horizons? (e.g., Campbell and Mankiw, 1987; Cochrane, 1988) Are observed asset returns "too volatile"? (e.g., Shiller, 1979; LeRoy and Porter, 1981) Are asset returns forecastable over long horizons? (e.g., Fama and French, 1988; Mark, 1995)

helpful comments, and the National Science Foundation and the Graduate School We develop regression-based tests of hypotheses about out of sample prediction errors. Representative tests include ones for zero mean and zero correlation between a prediction error and a vector of predictors. The relevant environments are ones in which predictions depend on estimated parameters. We show that standard regression statistics generally fail to account for error introduced by estimation of these parameters. We propose computationally convenient test statistics that properly account for such error. Simulations indicate that the procedures can work well in samples of size typically available, although there sometimes are substantial size distortions.

We develop general model-free adjustment procedures for the calculation of unbiased volatility loss functions based on practically feasible realized volatility benchmarks. The procedures, which exploit the recent non-parametric asymptotic distributional results in Barndorff-Nielsen and Shephard (2002a) along with new results explicitly allowing for leverage effects, are both easy-to-implement and highly accurate in empirically realistic situations. On properly accounting for the measurement errors in the volatility forecast evaluations reported in Andersen, Bollerslev, Diebold and Labys (2003), the adjustments result in markedly higher estimates for the true degree of return volatility predictability.

This paper describes some recent advances and contributions to our understanding of economic forecasting. The framework we develop helps explain the findings of forecasting competitions and the prevalence of forecast failure. It constitutes a general theoretical background against which recent results can be judged. We compare this framework to a previous formulation, which was silent on the very issues of most concern to the forecaster. We describe a number of aspects which it illuminates, and draw out the implications for model selection. Finally, we discuss the areas where research remains needed to clarify empirical findings which lack theoretical explanations.

: Revisions to GDP announcements are known to be quite large in all G-7 countries: many revisions in quarterly GDP growth are over a full percentage point at an annualized rate. In this paper, we examine the predictability of these data revisions. Previous work suggests that U.S. GDP revisions are largely unpredictable, as would be the case if the revisions reflect news not available at the time that the preliminary number is produced. We find that the degree of predictability varies throughout the G-7. For the U.S., the revisions are very slightly predictable, but for Italy, Japan and the UK, about half the variability of subsequent revisions can be accounted for by information available at the time of the preliminary announcement. For these countries, it appears that revisions reflect, to a significant degree, the removal of noise from the preliminary numbers, rather than the arrival of news. Keywords: Vintage data, preliminary data, final data, revision, GDP. # Division of Interna...

We propose a theoretical framework for assessing whether a forecast model estimated over one period can provide good forecasts over a subsequent period. We formalize this idea by defining a forecast breakdown as a situation in which the out-of-sample performance of the model, judged by some loss function, is significantly worse than its in-sample performance. Our framework, which is valid under general conditions, can be used not only to detect past forecast breakdowns but also to predict future ones. We show that main causes of forecast breakdowns are instabilities in the data generating process and relate the properties of our forecast breakdown test to those of structural break tests. The empirical application finds evidence of a forecast breakdown in the Phillips ’ curve forecasts of U.S. inflation, and links it to inflation volatility and to changes in the monetary policy reaction function of the Fed.

Regression-based tests of forecast probabilities of particular events of interest are constructed. The event forecast probabilities are derived from the SPF density forecasts of expected inflation and output growth. Tests of the event probabilities supplement statistically-based assessments of the forecast densities using the probability integral transform approach. The regression-based tests assess whether the forecast probabilities of particular events are equal to the true probabilities, and whether any systematic divergences between the two are related to variables in the agents ’ informa-tion set at the time the forecasts were made. Forecast encompassing tests are also used to assess the quality of the event probability forecasts.

We propose methods for evaluating density forecasts. We focus primarily on methods that are applicable regardless of the particular user's loss function. We illustrate the methods with a detailed simulation example, and then we present an application to density forecasting of daily stock market returns. We discuss extensions for improving suboptimal density forecasts, multi-step-ahead density forecast evaluation, multivariate density forecast evaluation, monitoring for structural change and its relationship to density forecasting, and density forecast evaluation with known loss function.

A major topic in empirical finance is correlation of default risk. Correlations are the main drivers for credit risk on a portfolio basis and for banks ’ capital requirements under the New Basel Accord. However, empirical evi-dence on the magnitude of correlations is rather scarce, mainly due to data limitations. Using a large database of bankruptcies in Germany we estimate correlations using a simple version of the Basel II factor model. Then we extend the model to an approach with observable risk factors and suggest that this model with default probabili-ties depending on the state of the economy may be more adequate. Empirical evidence on proxies for the credit cycles is presented for German industry sectors. We find that much of the co-movements can be explained by our variables. Finally, we discuss some implications for forecasts of distributions of potential future defaults of a bank’s portfolio. 1