This paper constructs a number of possible core measures of inflation using singular spectrum analysis (SSA). Annual changes in monthly inflation are decomposed into its trend, oscillatory and noise components in order to develop an understanding of the trend and cyclicality in South African headline inflation. Three cyclical components with differing amplitude and frequency are identified. The trend and cyclical components of inflation are found to be a good approximation of core inflation, the inertial part of inflation. These core measures are compared with other candidate core measures based on the properties of a good core inflation measure. Generally, the SSA measures outperform commonly used measures of core inflation based on both in‐ and out‐of‐sample performance.