…and all 11 of 11 such divergences arise because headline inflation jumps up or down with core inflation remaining stable.

One of the basics of macroeconomics is that (a0 core inflation is a better indictor of what headline inflation will be than headline inflation, and (b) that jumps in headline inflation carry next to no information about future values of either core or headline inflation:

In comments, PM informs us that this basic empirical fact is unknown to Stephen Williamson:

New Monetarist Economics: Core Inflation: In general, which prices are volatile and which are not will depend on the monetary policy regime and what the central bank is attempting to target….[T]he Fed could choose instead to target the prices of volatile-price goods…. The volatile prices are now smooth, the smooth prices are volatile, and the good forecasting tool for the future price level is the volatile price…. I don't see anything solid that justifies the Fed's focus on core inflation measures. Indeed, one could, I think, make a better case for looking at headline inflation measures.

Core inflation prices are smooth and food-and-energy prices volatile with a smooth money stock. To try to stabilize food-and-energy prices would require an unstable money stock--sending money into a deep nosedive to push down wages, etc. whenever the real price of energy rose, and sending money skyrocketing to push up wages, etc. whenever the real price of energy fell.

I can't see why anybody would think that a policy involving such instability in a control variable would be preferable to one with a smooth path of the control variable.

Am I missing something?