Summary

The Denton method is a well-known method for benchmarking. Its aim is to achieve consistency between time series on the same target variables that are measured at different frequencies (for instance annual data with quarterly data) with a different reliability. Following the literature, these periods will be called annual and sub-annual periods, respectively. This terminology can be used without loss of generality, sub-annual and annual periods can be any combination of two different periods with unequal lengths, such that one annual period covers a whole number of sub-annual periods.

The method may be applied to time series, consisting of at least one annual period. In achieving consistency, the sub-annual data are adjusted, while the annual data are not changed (i.e., at least not in the method that is originally described by Denton in 1971). Furthermore, the Denton method attempts to preserve the sub-annual changes of the high-frequency data as much as possible.

Originally, the Denton method is defined for univariate data. However, in the literature a lot of extensions are described, for instance for the multivariate case.

Mathematically, the Denton method translates a data reconciliation problem into a weighted quadratic optimisation problem under linear conditions. As mentioned by Bloem et al. (2001) the Denton method is very well suited for large-scale applications.

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