## A Newton's Method for Benchmarking Time Series According to a Growth Rates Preservation Principle

_IMF Working Papers, July 1, 2011_

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## Bibliographic details
- Authors: Marco Marini, Tommaso Di Fonzo
- Published: July 1, 2011
- Series: IMF Working Papers
- DOI: https://doi.org/10.5089/9781462311293.001

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### Summary
- Presents a new technique for temporally benchmarking a time series according to the growth rates preservation principle (GRP) by Causey and Trager (1981).
- Develops a procedure which:
  - (i) transforms the original constrained problem into an unconstrained one, and
  - (ii) applies a Newton's method exploiting the analytic Hessian of the GRP objective function.
- Claims the proposed technique is easy to implement, computationally robust and efficient, making it a plausible competitor of other benchmarking procedures (Denton, 1971; Dagum and Cholette, 2006) in data-production processes involving a considerable amount of series.

### Methodology and Technical Features
- Core principle: Growth Rates Preservation (GRP) criterion.
- Mathematical/algorithmic elements emphasized:
  - Newton’s method applied to the GRP objective function.
  - Use of the analytic Hessian matrix within the Newton framework.
  - Transformation from a linearly equality constrained non-linear optimization problem to an unconstrained minimization problem.
- Comparisons and benchmarks:
  - Positioned as competitor to Denton (1971) and Dagum and Cholette (2006) benchmarking procedures.
  - Mentions BFGS performance in keyword set (implying consideration of alternative optimization algorithms).

### Findings and Advantages
- The technique is:
  - Easy to implement.
  - Computationally robust.
  - Efficient for processing a considerable amount of series.
- The approach preserves movement/growth rates according to the GRP objective.

### Applications and Relevance
- Targeted at temporal benchmarking of time series where preservation of growth rates is desired.
- Suitable for data-production processes involving many series.
- Subject classifications: Artificial intelligence, Technology.
- Keywords: Artificial intelligence, benchmarked estimate, Benchmarking, benchmarking procedure, BFGS performance, Global, GRP criterion, GRP procedure, Hessian matrix, Linearly equality constrained non-linear optimization, minimization problem, Movement preservation, Newton’s method, objective function, optimization procedure, time series, WP

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