- Bikker R., Daalmans J., Mushudiani N. (2011) Macro Integration. Data reconciliation. Statistical methods (201104). The Hague/Heerlen, Statistics Netherlands.
Quality measure: Variance o f the reconciled indicators under condition that variances of the input high frequency numbers are known from external sources, through sampling, model - estimates or expert guesses.
Let us suppose that low frequency aggregated data of high accuracy is available, and is considered further as fixed. For example, annual estimates of some indicator. High frequency aggregated data is available from another source, and sums over its subsets should coincide with the elements of the low frequency data. For example, sums of the quarterly indicators should be equal to the values of annual indicators. The problem is to replace the high frequency data with new values which satisfy the restrictions of summation to the low frequency data, and differ as little as possible from the initial high frequency data in the sense of a quadratic distance function. The procedure used is called a reconciliation procedure and is formulated as a quadratic optimization problem with linear restrictions.