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A multivariate Denton method for Benchmarking Large Data Sets

A multivariate Denton method for Benchmarking Large Data Sets. Jacco Daalmans and Nino Mushkudiani 20 February 2009. Introduction. A man with one watch knows what time it is; a man with two watches is never quite sure. Outline. Introduction (Extended) Multivariate Denton method

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A multivariate Denton method for Benchmarking Large Data Sets

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  1. A multivariate Denton method for Benchmarking Large Data Sets Jacco Daalmans and Nino Mushkudiani 20 February 2009

  2. Introduction A man with one watch knows what time it is; a man with two watches is never quite sure

  3. Outline • Introduction • (Extended) Multivariate Denton method • Implementation • Conclusions

  4. Example: pro-rata method Quarter 1: 20 Quarter 2: 20 Quarter 3: 20 Quarter 4: 40 ------------------- Sum 100

  5. Example: pro-rata method Quarter 1: 20  Quarter 2: 20  Quarter 3: 20  Quarter 4: 40  ------------------- Sum 100  Year: 200

  6. Example: pro-rata method Quarter 1: 20  40 Quarter 2: 20  40 Quarter 3: 20  40 Quarter 4: 40  80 ------------------- Som 100  Year : 200

  7. Benchmarking • Adaptation of quarterly values, such that • ∑ Quarters = Year • Preservation of quarterly changes

  8. Drawback pro-rata method Year 1 | Year 2 | Year 3 | 200 100 OK 400

  9. Drawback pro-rata method Year 1 | Year 2 | Year 3 | 200 100 400

  10. Benchmarking • Denton method • ∑ Quarters = Year • Restrictions among time-series are satisfied. • Preservation of ALL quarterly changes (as good as possible)

  11. Drawback pro-rata method Year 1 | Year 2 | Year 3 | 200 100 400

  12. Drawback pro-rata method Year 1 | Year 2 | Year 3 | 200 100 400

  13. Multivariate Denton method • - Denton, Di Fonzo and Bikker. • - Quadratic programming (QP) • - Additive / Proportional model

  14. Extensions • Soft constraints -> Weights! • Ratio constraints -> Weights! • Inequalities -> • Fixed quarters -> Weights!

  15. Weights • Important tuning parameters! • Expressions that are easy to use • Requirements • 1) • 2) Invariance

  16. Implementation • Very large data sets! • QP- problems having • 160,000 variables • 75,000 constraints • - Prototype by using CPLEX • - Optimal solution found in 45 seconds

  17. Simulation study • - On Dutch supply and Use tables 2004-2006 • Cooperation with National Accounts employees • Results: • The most important economic relations could be included 2) Small differences with published outcomes.

  18. Conclusions • As a result of the simulation study we strongly expect that • the extended multivariate Denton method will be successfully implemented

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