Online Learning vs. TVP Forecast Combination

[This post is based on the first slide (below) of a discussion of Helene Rey et al., which I gave a few days ago at a fine NBER IFM meeting (program and clickable papers here). The paper is fascinating and impressive, and I'll blog on it separately next time. But the slide below is more of a side rant on general issues, and I skipped it in the discussion of Rey et al. to be sure to have time to address their particular issues.]

Quite a while ago I blogged here on the ex ante expected loss minimization that underlies traditional econometric/statistical forecast combination, vs. the ex post regret minimization that underlies "online learning" and related "machine learning" methods. Nothing has changed. That is, as regards ex post regret minimization, I'm still intrigued, but I'm still not persuaded.

And there's another thing that bothers me. As implemented, ML-style online learning and traditional econometric-style forecast combination with time-varying parameters (TVPs) are almost identical: just projection (regression) of realizations on forecasts, reading off the combining weights as the regression coefficients.  OF COURSE we can generalize to allow for time-varying combining weights, non-linear combinations, regularization in high dimensions, etc., and hundreds of econometrics papers have addressed and explored those issues. Yet the ML types seem to think they invented everything, and too many economists are buying it. Rey et al., for example, don't so much as mention the econometric forecast combination literature, which by now occupies large chapters of  leading textbooks, like Elliott and Timmermann at the bottom of the slide below.