Monday, August 16, 2021

Unconditional and Conditional Density Forecast Calibration

I have been reading a new paper by Tilman Gneiting and Johannes Resin (GR2021) -- deep and thought-provoking as always -- "Regression Diagnostics meets Forecast Evaluation:  Conditional Calibration, Reliability Diagrams, and Coefficient of Determination."

Their paper pushes in a variety of interesting ways toward aspects of conditional as opposed to merely unconditional (uniform probability transform, or PIT) density forecast calibration.    

That's largely what the iid part of the Diebold-Gunther-Tay (DGT 1998) result ("correct conditional calibration implies PIT ~ iid U(0,1)") is about, and DGT emphasize and illustrate that one needs to check not just the condition for correct unconditional calibration (PIT ~ U(0,1)), but rather the joint condition PIT ~ iid U(0,1).  

I want to understand more about the GR2021 results in their relation to the iid part of the DGT1998 PIT ~ iid U(0,1) result.      

Some relevant history and perspective are at

The GR2021 paper and code are at:;!!IBzWLUs!BtUAeIBxhkYOch-aPxSnALk9MfYczGKu4G37CXTTHnimafIb85ov4cY12xVEYhicRaVT$;!!IBzWLUs!BtUAeIBxhkYOch-aPxSnALk9MfYczGKu4G37CXTTHnimafIb85ov4cY12xVEYsNE2Kt1$

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