The inflation data has continued to be consistent with the forecast confidence limits since 2017, and the latest data out over a week ago is no different. It's true these confidence limits are pretty wide. Year over year inflation should've been between −0.1 and +4.0% last month according to the model (the value was 2.9%). Next month, the model says it should be between 0.0% and 4.1%. But this spread is comparable to the NY Fed's DSGE model for PCE inflation nearly two years out (which is a more stable measure than CPI). And the dynamic equilibrium model only has four parameters !
The solid red line is the original forecast and the dashed line shows an update of the shock parameters I made in March of this year (after the "lowflation" shock ended). As the change was negligible (i.e. well inside the confidence bands), it's shown for informational purposes. Below, I show continuously compounded (i.e. log derivative) and year over year changes in CPI (all items) along with the CPI level. (Click to enlarge.)
 Over the period from 2010 to 2020. If we include the data back to the 1960s, there is another shock adding three more parameters — but the contribution of those additional parameters has been exponentially suppressed since the 1990s.