Disease modelling has had considerable policy impact during the ongoing COVID-19 pandemic, and it is increasingly acknowledged that combining multiple models can improve the reliability of outputs. Here we report insights from ten weeks of collaborative short-term forecasting of COVID-19 in Germany and Poland (12 October–19 December 2020). The study period covers the onset of the second wave in both countries, with tightening non-pharmaceutical interventions (NPIs) and subsequently a decay (Poland) or plateau and renewed increase (Germany) in reported cases. Thirteen independent teams provided probabilistic real-time forecasts of COVID-19 cases and deaths. These were reported for lead times of one to four weeks, with evaluation focused on one- and two-week horizons, which are less affected by changing NPIs. Heterogeneity between forecasts was considerable both in terms of point predictions and forecast spread. Ensemble forecasts showed good relative performance, in particular in terms of coverage, but did not clearly dominate single-model predictions. The study was preregistered and will be followed up in future phases of the pandemic.

We report insights from ten weeks of collaborative COVID-19 forecasting for Germany and Poland (12 October – 19 December 2020). The study period covers the onset of the second wave in both countries, with tightening non-pharmaceutical interventions (NPIs) and subsequently a decay (Poland) or plateau and renewed increase (Germany) in reported cases. Thirteen independent teams provided probabilistic real-time forecasts of COVID-19 cases and deaths. These were reported for lead times of one to four weeks, with evaluation focused on one- and two-week horizons, which are less affected by changing NPIs. Heterogeneity between forecasts was considerable both in terms of point predictions and forecast spread. Ensemble forecasts showed good relative performance, in particular in terms of coverage, but did not clearly dominate single-model predictions. The study was preregistered and will be followed up in future phases of the pandemic.

We estimate a logit mixture vector autoregressive model describing monetary policy transmission in the euro area over the period 1999–2015. In contrast to other classes of nonlinear vector autoregressive models, regime affiliation is neither strictly binary, nor binary with a transition period, and based on multiple variables. We show that monetary policy transmission in the euro area can be described as a mixture of two states. In both states, output and prices are found to decrease after contractionary monetary policy shocks. However, the effects of monetary policy are less enduring in the “crisis state.”

The connection between regularization and min–max robustification in the presence of unobservable covariate measurement errors in linear mixed models is addressed. We prove that regularized model parameter estimation is equivalent to robust loss minimization under a min–max approach. On the example of the LASSO, Ridge regression, and the Elastic Net, we derive uncertainty sets that characterize the feasible noise that can be added to a given estimation problem. These sets allow us to determine measurement error bounds without distribution assumptions. A conservative Jackknife estimator of the mean squared error in this setting is proposed. We further derive conditions under which min-max robust estimation of model parameters is consistent. The theoretical findings are supported by a Monte Carlo simulation study under multiple measurement error scenarios.

We report on the second and final part of a pre-registered forecasting study on COVID-19 cases and deaths in Germany and Poland. Fifteen independent research teams provided forecasts at lead times of one through four weeks from January through mid-April 2021. Compared to the first part (October–December 2020), the number of participating teams increased, and a number of teams started providing subnational-level forecasts. The addressed time period is characterized by rather stable non-pharmaceutical interventions in both countries, making short-term predictions more straightforward than in the first part of our study. In both countries, case counts declined initially, before rebounding due to the rise of the B.1.1.7 variant. Deaths declined through most of the study period in Germany while in Poland they increased after a prolonged plateau. Many, though not all, models outperformed a simple baseline model up to four weeks ahead, with ensemble methods showing very good relative performance. Major trend changes in reported cases, however, remained challenging to predict.