Learning to average predictively over good and bad : comment on : using stacking to average Bayesian predictive distributions

We suggest to extend the stacking procedure for a combination of predictive densities, proposed by Yao, Vehtari, Simpson, and Gelman(2018), to a setting where dynamic learning occurs about features of predictive densities of possibly misspecified models. This improves the averaging process of good and bad model forecasts. We summarise how this learning is done in economics and finance using mixtures. We also show that our proposal can be extended to combining forecasts and policies. The technical tools necessary for the implementation refer to filtering methods from nonlinear time series and we show their connection with machine learning. We illustrate our suggestion using results from Ba̧stürk, Borowska, Grassi, Hoogerheide, and VanDijk(2018) based on financial data about US portfolios from 1928 until 2015.