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Typically, point forecasting methods are compared and assessed by means of an error measure or scoring function, with the absolute error and the squared error being key examples. The individual scores are averaged over forecast cases, to result in a summary measure of the predictive performance, such as the mean absolute error or the mean squared error. I demonstrate that this common practice can lead to grossly misguided inferences, unless the scoring function and the forecasting task are carefully matched. Effective point forecasting requires that the scoring function be specified ex ante, or that the forecaster receives a directive in the form of a statistical functional, such as the mean or a quantile of the predictive distribution. If the scoring function is specified ex ante, the forecaster can issue the optimal point forecast, namely, the Bayes rule. If the forecaster receives a directive in the form of a functional, it is critical that the scoring function be consistent for it, in the sense that the expected score is minimized when following the directive. A functional is elicitable if there exists a scoring function that is strictly consistent for it. Expectations, ratios of expectations and quantiles are elicitable. For example, a scoring function is consistent for the mean functional if and only if it is a Bregman function. It is consistent for a quantile if and only if it is generalized piecewise linear. Similar characterizations apply to ratios of expectations and to expectiles. Weighted scoring functions are consistent for functionals that adapt to the weighting in peculiar ways. Not all functionals are elicitable; for instance, conditional value-at-risk is not, despite its popularity in quantitative finance.

A statistical functional, such as the mean or the median, is called elicitable if there is a scoring function or loss function such that the correct forecast of the functional is the unique minimizer of the expected score. Such scoring functions are called strictly consistent for the functional. The elicitability of a functional opens the possibility to compare competing forecasts and to rank them in terms of their realized scores. In this paper, we explore the notion of elicitability for multi-dimensional functionals and give both necessary and sufficient conditions for strictly consistent scoring functions. We cover the case of functionals with elicitable components, but we also show that one-dimensional functionals that are not elicitable can be a component of a higher order elicitable functional. In the case of the variance, this is a known result. However, an important result of this paper is that spectral risk measures with a spectral measure with finite support are jointly elicitable if one adds the \"correct\" quantiles. A direct consequence of applied interest is that the pair (Value at Risk, Expected Shortfall) is jointly elicitable under mild conditions that are usually fulfilled in risk management applications.

We forecast quarterly US inflation based on the generalized Phillips curve using econometric methods that incorporate dynamic model averaging. These methods not only allow for coefficients to change over time, but also allow for the entire forecasting model to change over time. We find that dynamic model averaging leads to substantial forecasting improvements over simple benchmark regressions and more sophisticated approaches such as those using time varying coefficient models. We also provide evidence on which sets of predictors are relevant for forecasting in each period.

Managers have great discretion in determining forecast characteristics, but little is known about how managerial incentives affect these characteristics. This paper examines whether managers strategically choose forecast precision for self-serving purposes. Building on the prior finding that the market reaction to vague forecasts is weaker than its reaction to precise forecasts, we find that for management forecasts disclosed before insider sales, more positive (negative) news forecasts are more (less) precise than other management forecasts. The opposite applies to management forecasts disclosed before insider purchases. These results are consistent with managers strategically choosing forecast precision to increase stock prices before insider sales and to decrease stock prices before insider purchases. Additional analyses indicate that the impact of managerial incentives on forecast precision is less pronounced when institutional ownership is high or when disclosure risk is high, and is more pronounced when investors have difficulty in assessing the precision of managers' information.

In the practice of point prediction, it is desirable that forecasters receive a directive in the form of a statistical functional. For example, forecasters might be asked to report the mean or a quantile of their predictive distributions. When evaluating and comparing competing forecasts, it is then critical that the scoring function used for these purposes be consistent for the functional at hand, in the sense that the expected score is minimized when following the directive. We show that any scoring function that is consistent for a quantile or an expectile functional can be represented as a mixture of elementary or extremal scoring functions that form a linearly parameterized family. Scoring functions for the mean value and probability forecasts of binary events constitute important examples. The extremal scoring functions admit appealing economic interpretations of quantiles and expectiles in the context of betting and investment problems. The Choquet-type mixture representations give rise to simple checks of whether a forecast dominates another in the sense that it is preferable under any consistent scoring function. In empirical settings it suffices to compare the average scores for only a finite number of extremal elements. Plots of the average scores with respect to the extremal scoring functions, which we call Murphy diagrams, permit detailed comparisons of the relative merits of competing forecasts.

Survey respondents who make point predictions and histogram forecasts of macro-variables reveal both how uncertain they believe the future to be, ex ante, as well as their ex post performance. Macroeconomic forecasters tend to be overconfident at horizons of a year or more, but overestimate (i.e., are underconfident regarding) the uncertainty surrounding their predictions at short horizons. Ex ante uncertainty remains at a high level compared to the ex post measure as the forecast horizon shortens. There is little evidence of a link between individuals' ex post forecast accuracy and their ex ante subjective assessments.

Financial economics has posited a limited role for idiosyncratic noneconomic manager-specific influences, but the strategic management literature suggests such individual influences can affect corporate outcomes. We investigate whether individual managers play an economically significant role in their firms' voluntary financial disclosure choices. Tracking managers across firms over time, we find top executives exert unique and economically significant influence (manager-specific fixed effects) on their firms' voluntary disclosures, incremental to known economic determinants of disclosure, and firm- and time-specific effects. Managers' unique disclosure styles are associated with observable demographic characteristics of their personal backgrounds: managers promoted from finance, accounting, and legal career tracks, managers born before World War II, and those with military experience develop disclosure styles displaying certain conservative characteristics; and managers from finance and accounting and those with military experience favor more precise disclosure styles. These plausible associations confirm that our estimated manager-specific fixed effects capture systematic long-lived differences in managers' unique disclosure styles.

Forecast skill and potential predictability of 2-m temperature, precipitation rate, and sea surface temperature are assessed using 29 yr of hindcast data from models included in phase 1 of the North American Multimodel Ensemble (NMME) project. Forecast skill is examined using the anomaly correlation (AC); skill of the bias-corrected ensemble means (EMs) of the individual models and of the NMME 7-model EM are verified against the observed value. Forecast skill is also assessed using the root-mean-square error. The models’ representation of the size of forecast anomalies is also studied. Predictability was considered from two angles: homogeneous, where one model is verified against a single member from its own ensemble, and heterogeneous, where a model’s EM is compared to a single member from another model. This study provides insight both into the physical predictability of the three fields and into the NMME and its contributing models. Most of the models in the NMME have fairly realistic spread, as represented by the interannual variability. The NMME 7-model forecast skill, verified against observations, is equal to or higher than the individual models’ forecast ACs. Two-meter temperature (T2m) skill matches the highest single-model skill, while precipitation rate and sea surface temperature NMME EM skill is higher than for any single model. Homogeneous predictability is higher than reported skill in all fields, suggesting there may be room for some improvement in model prediction, although there are many regional and seasonal variations. The estimate of potential predictability is not overly sensitive to the choice of model. In general, models with higher homogeneous predictability show higher forecast skill.

Of the various renewable energy resources, wind power is widely recognized as one of the most promising. The management of wind farms and electricity systems can benefit greatly from the availability of estimates of the probability distribution of wind power generation. However, most research has focused on point forecasting of wind power. In this article, we develop an approach to producing density forecasts for the wind power generated at individual wind farms. Our interest is in intraday data and prediction from 1 to 72 hours ahead. We model wind power in terms of wind speed and wind direction. In this framework, there are two key uncertainties. First, there is the inherent uncertainty in wind speed and direction, and we model this using a bivariate vector autoregressive moving average-generalized autoregressive conditional heteroscedastic (VARMA-GARCH) model, with a Student t error distribution, in the Cartesian space of wind speed and direction. Second, there is the stochastic nature of the relationship of wind power to wind speed (described by the power curve), and to wind direction. We model this using conditional kernel density (CKD) estimation, which enables a nonparametric modeling of the conditional density of wind power. Using Monte Carlo simulation of the VARMA-GARCH model and CKD estimation, density forecasts of wind speed and direction are converted to wind power density forecasts. Our work is novel in several respects: previous wind power studies have not modeled a stochastic power curve; to accommodate time evolution in the power curve, we incorporate a time decay factor within the CKD method; and the CKD method is conditional on a density, rather than a single value. The new approach is evaluated using datasets from four Greek wind farms.

Central banks and other forecasters are increasingly interested in various aspects of density forecasts. However, recent sharp changes in macroeconomic volatility, including the Great Moderation and the more recent sharp rise in volatility associated with increased variation in energy prices and the deep global recession-pose significant challenges to density forecasting. Accordingly, this paper examines, with real-time data, density forecasts of U.S. GDP growth, unemployment, inflation, and the federal funds rate from Bayesian vector autoregression (BVAR) models with stochastic volatility. The results indicate that adding stochastic volatility to BVARs materially improves the real-time accuracy of density forecasts. This article has supplementary material online.