Benchmarking a system of time series : Denton's movement preservation principle vs a data based procedure

Most of the data obtained by statistical agencies have to be adjusted, corrected or somehow processed by statisticians in order to arrive at useful, consistent and publishable values. For example, the government agencies that collect and publish Quarterly National Accounts time series must produce subannual data that simultaneously comply with the relevant annual figures and satisfy accounting constraints (Eurostat, 1999). This kind of problem arises also when a system of time series is seasonally adjusted using a direct univariate approach, so that the accounting constraints valid for the raw series are not fulfilled (Di Fonzo and Marini, 2005). When temporally and contemporaneously aggregated series are known, temporal (e.g., between quarterly and annual data) and contemporaneous (between the quarterly aggregate and the sum of its component series) discrepancies can be eliminated using various reconciliation procedures. In this paper we consider (i) an extension of the univariate benchmarking approach by Denton (1971), founded on a well known movement preservation principle, and (ii) a data-based benchmarking procedure (Guerrero and Nieto, 1999) which exploits the autoregressive features of the preliminary series to be adjusted. In order to evaluate their performance in practical situations, both procedures are applied to simulated and real world data.