Definition: Multivariate two-steps methods
The starting point of multivariate two-steps methods is that a set of preliminary estimates for the aggregates of an account is available. The aggregates are subject to an accounting constraint that the preliminary series do not fulfil (e.g., the preliminary estimates for the components of GDP on the demand side do not sum to GDP, whose estimates has been obtained, for example, starting from output sources). Each series satisfied the temporal constraints (when annual figures are available). The problem consists then in distributing, according to a suitable criterion, the discrepancy between the quarterly preliminary values and the expected accounting quarterly constraint (often represented by a quarterly series). As in the univariate case, the distribution is made by minimising a quadratic loss function according to the same approach proposed by Denton, extended to the multivariate case (see Annex 11.A for more details).
Handbook on quarterly national accounts, 1999 Edition, Eurostat, p.258