RDP 2005-05: Underlying Inflation: Concepts, Measurement and Performance Equation

\begin{matrix} {\hat{π}}_{t}^{*} = \frac{\sum_{i = 1}^{N} \frac{w_{i t} π_{i t}}{{\hat{σ}}_{i}^{2}}}{\sum_{i = 1}^{N} \frac{w_{i t}}{{\hat{σ}}_{i}^{2}}} & for t = 1, \dots, T; and \end{matrix}

\begin{matrix} {\hat{σ}}_{i}^{2} = \frac{1}{T} \sum_{t = 1}^{T} w_{i t} {(π_{i t} - {\hat{π}}_{t}^{*})}^{2} & f o r i = 1, \dots, N . \end{matrix}