Tommaso Di Fonzo

The Estimation of M Disaggregate Time Series When Contemporaneous and Temporal Aggregates Are Known

We discuss the problem of estimating M (>1) high-frequency (say, quarterly or monthly) time series using the relevant low-frequency (say, annual or quarterly) data, the sum for each intra-annual period of the series to be estimated and, finally, a number of related indicators. The optimal (in least squares sense) estimator that fulfills both temporal and contemporaneous aggregation constraints is derived. In addition, we critically comment on the estimation approach followed by Rossi (1982), showing that a convenient reformulation of that method can be viewed as a special application of a known adjustment technique. Copyright 1990 by MIT Press.

On the Extrapolation with the Denton Proportional Benchmarking Method

Statistical offices have often recourse to benchmarking methods for compiling quarterly national accounts (QNA). Benchmarking methods employ quarterly indicator series (i) to distribute annual, more reliable series of national accounts and (ii) to extrapolate the most recent quarters not yet covered by annual benchmarks. The Proportional First Differences (PFD) benchmarking method proposed by Denton (1971) is a widely used solution for distribution, but in extrapolation it may suffer when the movements in the indicator series do not match consistently the movements in the target annual benchmarks. For this reason, an enhanced formula for extrapolation was recommended by the IMF’s Quarterly National Accounts Manual: Concepts, Data Sources, and Compilation (2001). We discuss the rationale behind this technique, and propose a matrix formulation of it. In addition, we present applications of the enhanced formula to artificial and real-life benchmarking examples showing how the extrapolations for the most recent quarters can be improved.

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

This work presents a new technique for temporally benchmarking a time series according to the growth rates preservation principle (GRP) by Causey and Trager (1981). A procedure is developed which (i) transforms the original constrained problem into an unconstrained one, and (ii) applies a Newtons method exploiting the analytic Hessian of the GRP objective function. We show that the proposed technique is easy to implement, computationally robust and efficient, all features which make it a plausible competitor of other benchmarking procedures (Denton, 1971; Dagum and Cholette, 2006) also in a data-production process involving a considerable amount of series.

Constrained retropolation of high-frequency data using related series: A simple dynamic model approach

The static approach by Chow and Lin (1971) to temporal disaggregation of an economic series by related indicators is extended to back-calculate high-frequency data constrained to their low-frequency counterpart according to a simple dynamic model.

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

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. Two widely used benchmarking procedures are the modified Denton Proportionate First Differences (PFD) and the Causey and Trager Growth Rates Preservation (GRP) techniques. In the literature it is often claimed that the PFD procedure produces results very close to those obtained through the GRP procedure. In this chapter we study the conditions under which this result holds, by looking at an artificial and a real-life economic series, and by means of a simulation exercise.

A Newton’s Method for Benchmarking Time Series

We present a Newton’s method with Hessian modification for benchmarking a time series according to a growth rates preservation principle. Unlike the well-known proportionate first differences solution by [7], this technique is based on a more natural measure of the movement of the preliminary series, whose dynamic profile is aimed to be preserved as much as possible by the benchmarked series. The computational issues arising from the nonlinearity of the problem can be dealt with by a computationally robust and efficient approach, which results in an effective statistical tool also in a data-production process involving a considerable amount of series.

Reconciliation of systems of time series according to a growth rates preservation principle

We propose new simultaneous and two-step procedures for reconciling systems of time series subject to temporal and contemporaneous constraints according to a growth rates preservation (GRP) principle. The techniques exploit the analytic gradient and Hessian of the GRP objective function, making full use of all the derivative information at disposal. We apply the new GRP procedures to two systems of economic series, and compare the results with those of reconciliation procedures based on the proportional first differences (PFD) principle, widely used by data-producing agencies. Our experiments show that (1) the nonlinear GRP problem can be efficiently solved through an interior-point optimization algorithm, and (2) GRP-based procedures preserve better the growth rates than PFD solutions, especially for series with high temporal discrepancy and high volatility.