Long and Ware
The Consumer Price Index measures the cost of the market basket for a typical urban American family. The reason why food and energy are not included is that they often have very volatile prices, while goods and services that are represented like housing, recreation, and medical care are more stable. For this reason, the CPI represented is known as "Core CPI". Inflation is an overall increase in prices of goods and services, which results in a higher priced market basket that is CPI.
According to the U.S. Bureau of Labor Statistics, significant increases and decreases in the CPI indicate periods of inflation and deflation over a short time frame. Both graphs represent this through quarterly percent change, from quarter to quarter, over the past five years.
The above graphs provide supporting evidence for the relationship between CPI increases and inflation, as well as CPI decreases and deflation. For inflation, three significant peaks occur in Q2 2015, Q2 2016, and Q4 2016. Three peaks also occur for CPI in Q2 2015, Q2 2016, and Q1 2017. It is evident that there is a relationship between they are the same for the first two and a quarter difference for the third. For the troughs, which show deflation, occur in Q4 2014, Q3 2015, Q3 2016, and Q2 2017. As for significant decreases in CPI, they occur in Q3 2014, Q3 2015, Q3 2016, Q3 2017. All are within a quarter difference of the other, showing a significant relationship. The peaks and troughs noted show that there is, in fact, a strong relationship between inflation and the CPI.
The Prof: I add here a graph of core CPI QoQ inflation using seasonally adjusted data. As you can see, the peaks and troughs are quite different. An alternative to using seasonally adjusted data is to use the unadjusted data but with the percent change YoY (year over year) rather than QoQ.
More later on what the "breakeven inflation measure" represents – it's a government bond-derived measure so is not quite what it sounds like.
U.S. Bureau of Labor Statistics, Consumer Price Index for All Urban Consumers: All Items [CPIAUCSL], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/CPIAUCSL, January 18, 2018.