Core inflation represents the long run trend in the price level. In measuring long run inflation, transitory price changes should be excluded. One way of accomplishing this is by excluding items frequently subject to volatile prices, like food and energy.
The preferred measure by the Federal Reserve of core inflation in the United States is the change in the core Personal consumption expenditures price index (PCE). This index is based on a dynamic consumption basket. Economic variables adjusted by this price deflator are expressed in chained dollars, rather than the alternative constant-dollar measure based on a fixed goods' basket.
Since February 2000, the Federal Reserve Board’s semiannual monetary policy reports to Congress have described the Board’s outlook for inflation in terms of the PCE. Prior to that, the inflation outlook was presented in terms of the CPI. In explaining its preference for the PCE, the Board stated: The chain-type price PCE index draws extensively on data from the consumer price index but, while not entirely free of measurement problems, has several advantages relative to the CPI. The PCE chain-type index is constructed from a formula that reflects the changing composition of spending and thereby avoids some of the upward bias associated with the fixed-weight nature of the CPI. In addition, the weights are based on a more comprehensive measure of expenditures. Finally, historical data used in the PCE price index can be revised to account for newly available information and for improvements in measurement techniques, including those that affect source data from the CPI; the result is a more consistent series over time. —Monetary Policy Report to the Congress, Federal Reserve Board of Governors, Feb. 17, 2000
Previously the Federal Reserve had used the US Consumer Price Index as its preferred measure of inflation. The CPI is still used for many purposes, for example, for indexing social security. The equivalent of the CPI is also commonly used by central banks of other countries when measuring inflation. The CPI is presented monthly in the US by the Bureau of Labor Statistics. This index tends to change more on a month to month basis than does "core inflation". This is because core inflation eliminates products that can have temporary price shocks (i.e. energy, food products). Core inflation is thus intended to be an indicator and predictor of underlying long-term inflation.
The concept of core inflation as aggregate price growth excluding food and energy was introduced in a 1975 paper by Robert J. Gordon. This is the definition of "core inflation" most used for political purposes. Core inflation was also developed and advocated by Otto Eckstein, in (Eckstein 1981).
Moving average 
There are also other types of measuring inflation rates. In the United States the Dallas Federal Reserve computes a trimmed mean PCE price index, which separates "noise" and "signal". This is trimmed at 19.4% at the lower tail end and 25.4% at the upper tail. The Cleveland Federal Reserve computes a Median CPI and a 16% trimmed mean CPI. Trimmed means that the highest rises and declines in prices are trimmed by a certain percentage, attributing to a more accurate measurement on core inflation.
In relation to this, the Median CPI is usually higher than the trimmed figures for both PCE and CPI. There also is a median PCE, but is not widely used.
See also 
- Gordon, Robert J. (1975). "Alternative Responses of Policy to External Supply Shocks". Brookings Papers on Economic Activity (Brookings Papers on Economic Activity, Vol. 1975, No. 1) 6 (3): 183–206. doi:10.2307/2534065. JSTOR 2534065.
- Robert Rich, Charles Steindel (2005). A Review of Core Inflation and an Evaluation of Its Measures (Staff Report, Federal Reserve Bank of New York).  
- Eckstein, Otto (1981). Core inflation
- Core Inflation: A Review of Some Conceptual Issues, Mark A.Wynne, Federal Reserve Bank of St. Louis Review, May/June 2008
- OECD inflation statistics
- Core Logic, Paul Krugman, February 26, 2010 – explanation of concept and motivation