A Polynomial Method for Temporal Disaggregation of Multivariate Time Series

Abstract

A problem often encountered in the preparation of economic and business time series is that much of current data is only available in aggregate form. For example, we rarely see daily or weekly production data, but only monthly or quarterly figures. There has been considerable research done on the disaggregation of univariate time series. However, in the multivariate case, we find only little research (e.g., Di Fonzo, 1990; Rossi, 1982, etc.). An example of temporal disaggregation in the multivariate case is the problem of estimating quarterly consumption series for some categories of consumer goods using yearly observations of each category and quarterly values of total consumer's expenditure. This article considers the problem of temporal disaggregation in the multivariate case. The problem considered here is the estimation of M (> 1) high-frequency time series using the relevant low-frequency data. The M estimated high-frequency time series must fulfill both temporal and contemporaneous aggregation constraints. An econometric computer package G, developed by Almon (1988), provides an univariate polynomial method to convert annual series to quarterly figures by interpolation. In this article, we propose a procedure which extend the polynomial method (Almon, 1988) to the multivariate case. The proposed method is used in the case of temporal disaggregation of multivariate time series when related series are not available. Previous work in the multivariate case have dealt with the same problem but only when related series are available. The first section of the article is devoted to the formulation of the problem in the univariate and multivariate case, while the second section gives the details of the method we propose. The method is illustrated through the example of deriving quarterly US Gross Domestic Product by major type of product from the annual series.

Keywords:

• Interpolation
• Polynomial method
• Temporal and contemporaneous aggregation constraints
• Temporal disaggregation

Mathematics Subject Classification:

• 65D05
• 93E14
• 65D10
• 57R12

View correction statement:

Erratum

Notes

¹Eurostat (1999) contains a survey, taxonomy, and description of the main temporal disaggregation methods proposed in the literature. Bloem et al. (2001) devoted two chapters for the analysis of the relevant techniques to be used for benchmarking, extrapolation, and related problems occurring in the compilation of quarterly national accounts.

²The program is available upon request.

^aGoods.

^bIncludes government consumption expenditures, which are for services (such as education and national defense) produced by government. In current dollars, these services are valued at their cost of production.

^cStructures.