Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization

Estimation du PIB mensuel canadien : 1962 à 1985

“…Il n'était pas approprié de retenir les techniques de Denton (1971), Fernandez (1981), et Litterman (1983 Le tableau 3 présente les résultats de l'estimation de l'équation de prix. Aucune autocorrélation résiduelle n'est significative.…”

Benchmarking and Movement Preservation: Evidences from Real-Life and Simulated Series

“…On the other hand, r 1 can be seen as the ratio between the Mean Absolute Adjustments: sometimes this index can be larger than 1, thus indicating a better performance of Denton P F D when the size of the corrections to the preliminary growth rates is measured according to an absolute rather than a squared form. The first example we consider is the artificial preliminary series used in the seminal paper of Denton (1971). It consists of a five-year artificial quarterly series, with a fixed seasonal pattern invariant from year to year.…”

“…Thus in what follows we consider two procedures designed to preserve at the best the movement of the series p t : modified Denton P F D and Causey and Trager GRP 1 . Denton (1971) proposed a benchmarking procedure grounded on the Proportionate First Differences between the target and the original series. Cholette (1984) slightly modified the result of Denton, in order to correctly deal with the starting conditions of the problem.…”

“…In section 2 the two benchmarking procedures are described, and the way they take into account a 'movement preservation principle' is discussed. In section 3 the artificial time series of Denton (1971) and a quarterly preliminary series of the EU Quarterly Sector Accounts (Di Fonzo and Marini, 2009) are benchmarked to their annual counterparts, using both modified Denton P F D and Causey and Trager GRP benchmarking procedures, and the results are discussed. In section 4 we design a simulation exercise in order to analyze the distinctive features of the two procedures.…”

“…The benchmarking problem arises when time series data for the same target variable are measured at different frequencies with different level of accuracy, and there is the need to remove discrepancies between annual benchmarks and corresponding sums of the sub-annual values. The most widely used benchmarking procedures are the modified Denton Proportional First Differences (P F D) technique (Denton, 1971;Cholette, 1984), and the Causey and Trager (1981) Growth Rates Preservation (GRP ) procedure (see also Trager, 1982, and Bozik and Otto, 1988). The P F D procedure looks for benchmarked estimates aimed at minimizing the sum of squared proportional differences between the target and the unbenchmarked values, and is characterized by an explicit benchmarking formula involving simple matrix operations.…”