The latest core CPI data came out today and is up on FRED. I thought I'd post a picture of the model results without smoothing as I did for the PCE numbers that came out at the beginning of the month. However I noticed a pretty obvious lag in the CPI data relative to the model (there is no obvious lag in the PCE inflation data [1]), so I decided to try and do a four-parameter fit with a lag

*y0*(along with*α*,*m0*and*γ*-- see paper).
Overall, it works pretty well (model = blue, data = green and 1-sigma error bands) with the lag being

*y0*= 1.2 years:And here's a zoom to the last 15 years:

If the lag is correct, then the model gives the future values of core CPI (past the vertical line) using data available today.

**Update**

Although less obvious, the lag has the opposite sign for Japan (

*y0*= -0.9):...

**Footnotes:**

[1] Here is the graph for reference:

One interesting thing is that maybe PCE inflation measures CPI inflation y0 = 1.2 years in the future -- which might (partially) explain why PCE inflation comes in about 0.3 percentage points lower (per Scott Sumner).

Wow, interesting!

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