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Definition: Multivariate optimal methods

National accounts

As in the univariate case, the multivariate optimal approach supplies the estimates of a set of aggregates related by an account constraint according to a statistically optimal approach. The main idea is the same as in the univariate case: the related quarterly series are used in a multivariate regression model to obtain the estimation of the aggregate  quarterly series with respect of both the temporal (versus the annual known aggregate series) and quarterly contemporaneous-accounting constraints (e.g. the constraint may correspond to the quarterly series of GDP). The optimal multivariate estimation approach offers a natural and coherent solution to the interpolation, balancing and extrapolation problems.  The method derives from the univariate techniques of Chow and Lin. Two different techniques have been developed, the difference being the structure of the error in the regression model. The two forms of the stochastic error process considered are:
 - multivariate white noise;
 - multivariate random walk.
The extrapolation is carried out according to the same principles of the univariate case: given the new values of the relates series, the optimal now cast are directly obtained from the quarterly regression model.
Handbook on quarterly national accounts, 1999 Edition, Eurostat, p.258