The predictive likelihood is of particular relevance in a Bayesian setting when the purpose is to rank models in a forecast comparison exercise. This paper discusses how the predictive likelihood can be estimated for any subset of the observable variables in linear Gaussian state-space models...

This paper shows how to compute the h-step-ahead predictive likelihood for any subset of the observed variables in parametric discrete time series models estimated with Bayesian methods. The subset of variables may vary across forecast horizons and the problem thereby covers marginal and joint...

Density forecast combinations are examined in real-time using the log score to compare five methods: fixed weights, static and dynamic prediction pools, as well as Bayesian and dynamic model averaging. Since real-time data involves one vintage per time period and are subject to revisions, the...

We compare real-time density forecasts for the euro area using three DSGE models. The benchmark is the Smets-Wouters model and its forecasts of real GDP growth and inflation are compared with those from two extensions. The first adds financial frictions and expands the observables to include a...

This paper provides a detailed description of an extended version of the ECB’s New Area-Wide Model (NAWM) of the euro area (cf. Christoffel, Coenen, and Warne 2008). The extended model—called NAWM II—incorporates a rich financial sector with the threefold aim of (i) accounting for a...

It is standard in applied work to select forecasting models by ranking candidate models by their PMSE in simulated out-of-sample (SOOS) forecasts. Alternatively, forecast models may be selected using information criteria (IC). We compare the asymptotic and finite-sample properties of these...

It is widely known that significant in-sample evidence of predictability does not guarantee significant out-of-sample predictability. This is often interpreted as an indication that in-sample evidence is likely to be spurious and should be discounted. In this paper we question this conventional...

We compare real-time density forecasts for the euro area using three DSGE models. The benchmark is the Smets-Wouters model and its forecasts of real GDP growth and inflation are compared with those from two extensions. The first adds financial frictions and expands the observables to include a...

This paper provides a detailed description of an extended version of the ECB's New Area-Wide Model (NAWM) of the euro area (cf. Christoffel, Coenen, and Warne 2008). The extended model - called NAWM II - incorporates a rich financial sector with the threefold aim of (i) accounting for a genuine...

Density forecast combinations are examined in real-time using the log score to compare five methods: fixed weights, static and dynamic prediction pools, as well as Bayesian and dynamic model averaging. Since real-time data involves one vintage per time period and are subject to revisions, the...