Core PCE is the series in the summary-of-economic-projections and the one Fed speakers cite. A further cut, core services excluding housing, is often called supercore and is watched as the component most tied to wage growth.
Because so much of it is imputed or lagged, core PCE turns slowly. That is a feature for a policy target and a problem for a trader, since by the time the twelve-month rate confirms a trend the three and six-month annualised rates have usually been telling the story for a while.
Example: monthly core PCE prints of 0.17%, 0.13% and 0.15% annualise to about 1.8%, even though the year-over-year rate still reads 2.8% because of large prints twelve months earlier. That gap is a base-effects story.
Related: pce-price-index, core-cpi, base-effects, summary-of-economic-projections, average-hourly-earnings