["Oxford Bulletin of Economics and Statistics, EarlyView. ", "\nABSTRACT\nThis paper discusses asymptotic and bootstrap confidence intervals for multivariate permanent‐transitory decompositions of cointegrated vector autoregressive I(1) systems, with a focus on price discovery. Alternative estimators of the permanent components are compared in terms of efficiency also under separable linear restrictions on the parameters, and it is found that the one based on model residuals is most efficient. Bootstrap implementations are discussed and compared. Asymptotic results are also derived for information and component shares widely used in price discovery to measure the relative importance of different markets. A Monte Carlo study and an application illustrate the findings.\n"]