I'm not a big fan of the PCE, because it is a chained price index. It all boils down to is that it includes the effects of consumers switching to lower grade items, so, for example if in the face of high beef prices, consumers switch to chicken and beans, that lowers the reported meat and food PCE inflation numbers. (The reverse also happens too)
For that reason, I prefer the CPI, which has less of that.
But the PCE, especially the Core PCE, is what the Fed favors, so anyone trying to predict what the Fed might do needs to focus on the Core PCE, and not the CPI measures
I suspect the Fed prefers the PCE with its chained-price shenanigans because it comes in lower than the CPI, thus, it's easier for them to reach their 2% target.
The Fed favors the CORE measures for forecasting FUTURE inflation, as shown by analysis of the data.
I annualize them all to be easy to compare to each other, and to compare to the FED's 2% goal. I use the actual index values rather than the one-digit changes that are commonly reported in the media. Links to the data are with the graphs.
All the numbers were revised beginning January 2021 or maybe even back earlier (my data for producing the graphs, scraped from the FRED sites, goes back to January 2021.
ALL the numbers are the seasonally adjusted ones
In below, "REG" is the regular PCE (all items).
While "CORE" is the Core PCE (all items less food and less energy)
REG CORE
--- ----
3.2% 2.8% July to August change, annualized
2.9% 2.9% 3 month average, annualized
2.7% 2.9% 12 month average, aka year-over-year
Fed target is 2.0%
REGULAR ALL ITEMS PCE
BEA.gov News release: https://www.bea.gov/ and click on "Personal Income and Outlays" or "Personal Income"
https://www.bea.gov/news/2025/personal-income-and-outlays-august-2025
https://fred.stlouisfed.org/series/PCEPI

CORE PCE:
https://fred.stlouisfed.org/series/PCEPILFE

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For comparison purposes, here are the CPI graphs
REGULAR ALL ITEMS CPI (released 9/11/25)
https://www.bls.gov/news.release/cpi.nr0.htm
https://data.bls.gov/timeseries/CUSR0000SA0

CORE CPI (released 9/11/25):
http://data.bls.gov/timeseries/CUSR0000SA0L1E

LBN thread on CPI inflation,9/11/25:
https://www.democraticunderground.com/10143528031