The measurement of core inflation can be carried out by optimal signal extraction techniques based on the multivariate local level model, by imposing suitable restrictions on its parameters. The various restrictions correspond to several specialisations of the model:the core inflation measure becomes the optimal estimate of the common trend in a multivariate time series of inflation rates for a variety of goods and services, or it becomes a minimum variance linear combination of the inflation rates, or it represents the component generated by the common disturbances in a dynamic error component formulation of the multivariate local level model. Particular attention is given to the characterisation of the optimal weighting functions and to the design of signal extraction filters that can be viewed as two sided exponentially weighted moving averages applied to a cross-sectional average of individual inflation rates. An empirical application relative to U.S. monthly inflation rates for 8 expenditure categories is proposed.