A Generalization of Initial Conditions in Benchmarking of Economic Time-Series by Additive and Proportional Denton Methods

The paper presents unified analytical solution for combining high-frequency and low-frequency economic time-series by additive and proportional Denton methods with parametrical dependence on the initial values of variable and indicator in evident form. This solution spans Denton’s original and Cholette’s advanced benchmarking initial conditions as the subcases. Computational complexity of the obtained solution is associated with inversion of a square matrix of the order that is equal to the number of low-frequency observations available. Practical applying the proposed solution under data revisions allows to construct suboptimal concatenation of frozen and newly revised parts of benchmarked time-series by using the last benchmarked-to-indicator ratio (or benchmarked and indicator difference in additive case) from the range of data fixed as initial condition for benchmarking or re-benchmarking the newly revised data by the proportional (or additive) Denton method.