Title: Various algorithmic approaches for the balancing problem
Authors: Susie Fortier - Statistics Canada (Canada) [presenting]
Michel Ferland - Statistics Canada (Canada)
Abstract: Time series data produced by National Statistical Offices and Systems of National Accounts must often respect a vast array of accounting relationships. These relationships can be quite simple, such as requiring that regional components add up to a national total or more complex, such as the econometric equalities that may be used to compute the Gross Domestic Product. As the data may come from various sources or undergo non-linear data processing such as seasonal adjustment, the accounting relationships must often be restored before publication. The process used to restore the accounting coherence in the data is referred to as balancing or reconciliation. The problem can be approached in various ways ranging from a purely numerical point of view to a fully parameterised model. Several solutions will be presented and discussed. From a regression-based model solved through matrix manipulation to a mathematical optimisation problem solved numerically, the algorithmic approaches will be compared with emphasis on their strengths and weaknesses. Statistics Canada's recent implementation of a numerical optimisation solution as part of their G-Series software will also be presented.