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In the U.S., core inflation is total inflation minus the volatile components of energy and food. Core inflation is used to capture the overall trend of total inflation, which is very important due to its effect on monetary policy especially with respect to forecasting future inflation. This book examines whether core inflation has been able to capture the overall trend of total inflation by using both the real-time personal consumption expenditure (PCE) and the Consumer Price Index (CPI) as measures of inflation. The frontier nonparametric methods presented in this book are able to shed more light on the relationship between total inflation and core inflation than the traditional parametric methodology as it pertains to the study of inflation persistence.