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

Document Type : Research Paper

Author

National Research University “Higher School of Economics”, Moscow, Russian Federation

Abstract

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.

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References

1. Bloem, A.M., Dippelsman, R.J. and Maehle, N.O. (2001). Quarterly National Accounts Manual: Concepts, Data Sources, and Compilation. Washington, D.C.: International Monetary Fund.
2. Cholette, P.A. (1979). Adjustment methods of sub-annual series to yearly benchmarks. Proceedings of the Computer Science and Statistics, 12th Annual Symposium on the Interface.University of Waterloo, 358 – 366.
3. Dagum, E.B. and Cholette, P.A. (2006). Benchmarking, Temporal Distribution, and Reconciliation Methods for Time Series: Lecture Notes in Statistics #186. New York: Springer Science+Business Media.
4. Denton, F.T. (1971). Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization. Journal of the American Statistical Association, 66, No. 333, 99 – 102.
5. Magnus, J.R. and Neudecker, H.  (2007). Matrix Differential Calculus with Applications in Statistics and Econometrics, 3d ed. Chichester, UK, John Wiley & Sons.
Iranian Economic Review
Volume 19, Issue 3 - Serial Number 3
December 2015
Pages 251-264

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