Overall, CPI lags at least 4-6 month. However, the different components of CPI lags to varying degrees. The worst is home prices and rent, which lags a HUGE 9-12 months. And this component makes up almost half of the CPI calculation. Bottom line.....CPI lags big time. PPI is a little better, but still lags as well.
However, the biggest BS is using year over year calculations to gauge what is going on today. That's stupid people not understanding simple math. YoY is essentially a rolling-12 month average. What happened 12 months ago carries the same value/importance as the current month. WTF?
YoY (or in my business we say MAT.....moving annual total) should not be used for real-time decisions or adjustments. It blinds the current trend and doesn't give a realistic view of what is going on today. Gotta stick with MoM instead.
Using YoY is why Powell missed all the inflation in 2021 and is now missing that fact that inflation has been essentially flat for 2 months and counting.