Here is a graph from FRED showing monthly percentage movements of core inflation. (link to data)
There used to be ranges that core inflation moved within. The monthly change either hit the maximum of that range or the minimum with some breakout movements in between. Monthly movements made sense by looking at 12-month moving averages.
Since about the year 2000, the visible ranges have disappeared. The monthly movements are more free-form. Thus monthly core inflation numbers should be more accurate now. However, there is still noise in the movements which belie that prices are sticky and should not change so erratically.
The best way to view monthly inflation numbers is with "Annualized" moving averages as Tim Duy does. Here is an example from Tim Duy.
Look at the time period from mid-2010 to mid-2011. You see large positive monthly movements in the second half of 2010 but the 12-month moving average was rising much more slowly. In the first half of 2011, inflation was coming down, but the 12-month moving average was still rising and kept rising until mid-2011. So the noisy monthly movements were designed to keep the 12-month moving average on a steadily rising trend.
Discerning the correct and steady trend of core inflation is the key.
Back in the early 80's, my undergrad teacher would use an 18-month moving average. But if we knew which monthly moving average is being manipulated on a monthly basis, we would understand each monthly change better.