Clark and McCracken (2008) argue that combining real-time point forecasts from VARs of output, prices and interest rates improves point forecast accuracy in the presence of uncertain model instabilities. In this paper, we generalize their approach to consider forecast density combinations and evaluations. Whereas Clark and Mc-Cracken (2008) show that the point forecast errors from particular equal-weight pairwise averages are typically comparable or better than benchmark univariate time series models, we show that neither approach produces accurate real-time forecast densities for recent US data. If greater weight is given to models that allow for the shifts in volatilities associated with the Great Moderation, predictive density accuracy improves substantially.

We argue that the next generation of macro modellers at Inflation Targeting central banks should adapt a methodology from the weather forecasting literature known as ‘ensemble modelling’. In this approach, uncertainty about model specifications (e.g., initial conditions, parameters, and boundary conditions) is explicitly accounted for by constructing ensemble predictive densities from a large number of component models. The components allow the modeller to explore a wide range of uncertainties; and the resulting ensemble ‘integrates out ’ these uncertainties using time-varying weights on the components. We provide two examples of this modelling strategy: (i) forecasting inflation with a disaggregate ensemble; and (ii) forecasting inflation with an ensemble DSGE.

Combined density nowcasts for quarterly Euro-area GDP growth are produced based on the real-time performance of component models. Components are distinguished by their use of “hard ” and “soft ” indicators. We consider the accuracy of the density nowcasts as within-quarter information on the monthly indicators accumulates. We focus on their ability to anticipate the recent recession probabilistically. We find that the relative utility of “soft ” data increased suddenly during the recession. But as this instability was hard to detect in real-time it helps, when producing nowcasts knowing only one month’s “hard ” data, to weight the different indicators equally. As more monthly “hard ” data arrive, better calibrated densities are obtained by giving a higher weight in the combination to these “hard ” indicators.

A popular macroeconomic forecasting strategy takes combinations across many models to hedge against model instabilities of unknown timing; see (among others) Stock & Watson (2004), Clark & McCracken (2009), and Jore, Mitchell and Vahey (2009). The scope of such ensemble forecasting exercises usually excludes Dynamic Stochastic General Equilibrium (DSGE) models, such as those advocated by Del Negro and Schorfheide (2004) and Smets and Wouters (2007), limiting the computational burden. In this paper, we use an expert combination framework (Winkler, 1981) to combine forecast densities from Vector Autoregressions (VARs), and a DSGE model (NEMO: the Norges Bank core policymaking macromodel). We show that the predictive densities from the DSGE model are competitive with those from a VAR ensemble if the VAR components are restricted to have constant parameters. In this case, both the VAR ensemble and the DSGE forecast densities are poorly calibrated. However, a VAR ensemble which encompasses structural break components produces well-calibrated forecast densities. The VARs with breaks are

In this paper we use U.S. real-time vintage data and produce combined density nowcasts for quarterly GDP growth from a system of three commonly used model classes. The density nowcasts are combined in two steps. First, a wide selection of individual models within each model class are combined separately. Then, the nowcasts from the three model classes are combined into a single predictive density. We update the density nowcast for every new data release throughout the quarter, and highlight the importance of new information for the evaluation period 1990Q2-2010Q3. Our results show that the logarithmic score of the predictive densities for U.S. GDP increase almost monotonically as new information arrives during the quarter. While the best performing model class is changing during the quarter, the density nowcasts from our combination framework is always performing well both in terms of logarithmic scores and calibration tests. The density combination approach is superior to a simple model selection strategy and also performs better in terms of point forecast evaluation than standard point forecast combinations.