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

with several members of the “Economic Analysis and Forecasting Department ” at the Banco de España. We would also like to thank, without implicating, Samuel Hurtado, Gabriel Perez-Quiros and Alberto Urtasun for comments and suggestions at the earliest stage of the work. DISCLAIMER: The views expressed in this paper are the author’s, not those of Banco de España. Documentos de Trabajo. N.º 1037 2010 The Working Paper Series seeks to disseminate original research in economics and fi nance. All papers have been anonymously refereed. By publishing these papers, the Banco de España aims to contribute to economic analysis and, in particular, to knowledge of the Spanish economy and its international environment. The opinions and analyses in the Working Paper Series are the responsibility of the authors and, therefore, do not necessarily coincide with those of the Banco de España or the Eurosystem. The Banco de España disseminates its main reports and most of its publications via the INTERNET at the following website: