Interval Prediction

Last time I blogged on Serena's amazing presentation from Per's Chicago meeting,
https://fxdiebold.blogspot.com/2019/10/large-dimensional-factor-analysis-with.html

But I was equally blown away by Rina's amazing "Predictive inference with the jackknife+".
Rina Foygel Barber∗ , Emmanuel J. Canes† , Aaditya Ramdas‡ , Ryan J. Tibshirani‡§
https://arxiv.org/pdf/1905.02928.pdf.

Correctly calibrated prediction intervals despite arbitrary model misspecification!

Of course I'm left with lots of questions.  They have nice correct-coverage theorems. What about length?  I would like theorems (not just simulations) as regards shortest length intervals with guaranteed correct coverage. Their results seem to require iid or similar exchangability environments. What about heteroskedastic environments where prediction error variance depends on covariates? What about time series environments?

Then, quite amazingly, "Distributional conformal prediction" by Victor Chernozukov et al., arrived in my mailbox.
https://arxiv.org/pdf/1909.07889.pdf
It is similarly motivated and may address some of my questions.

Anyway, great developments for interval prediction!