This article advances the theory and methodology of signal extraction by developing the optimal treatment of difference stationary multivariate time-series models. Using a flexible time-series structure that includes co-integrated processes, we derive and prove formulas for minimum mean square error estimation of signal vectors in multiple series, from both a finite sample and a bi-infinite sample. As an illustration, we present econometric measures of the trend in total inflation that make optimal use of the signal content in core inflation.