Similar methodologies in calculating Inflation & inflation % changes are too simplistic. These are methodologies based on index formulas that in the end calculate the sum of weighted % changes and are cumulative. The FRED CPI INDEX chart explains, quite well, the quasi exponential growth of the CPI Index, by design of its Summation % changes methodology. That fails to understand Price Inflation changes even at times of low & moderate price increases when Inflation in % tends to Central Banks 2.0% benchmark. Thereby, Monetary Policies have been misplaced.
The methodology design to measure Inflation requires observing supply & demand market data, with commodities prices, while also measuring Demand Elasticity and Inelasticity (-q’p/q), to then approximate Price levels for goods. Indeed, Statistical Multivariate methodology with Variance, Covariance and correlation, of goods prices % changes. Multivariate regression allows for determining how far Theta, Variance of certain parameters fluctuate (sigma/sqrt(n)) standard errors from the 2.0% inflation price stability, thereby combining those variables with the Central Banks money market interest rate tool, in understanding & modelling, going forward, the appropriate interest rate levels. This CPI Index chart started with 21.48 points in January 1947, to April 2022 with CPI 288.663 points.
CPI INDEX Variance explains the Inflationary spirals of exponential growth of prices
Var= 660450% thousand, Standard Deviation=81286% thousand. So the Average CPI Index value, with this methodology, should be 114.99= 115 points, basically, the CPI INDEX INFLATED 173.66 points, that in $dollar economic terms it’s way more than 8.5% CPI measured in 2022.
In fact, starting with 21.48 points to 288.663 points the CPI Index Inflated 13.44 times, INFLATED 1344% thousand. The mode value of this dataset = 29.84.
Consumer Price Index for All Urban Consumers: Purchasing Power of the Consumer Dollar in U.S. City Average 1947-2022 series.
The USDollar and U.S. citizens have constantly lost Purchasing Power, while the economy Inflated away, between economic growth periods and recessions.