Methodological Aspects of Time Series Back-Calculation

Abstract

This paper provides the theoretical and operational framework for estimating past values of relevant time series starting from a (limited) information set. We consider a general approach that includes as special cases time series aggregation and temporal and/or spatial disaggregation problems. Furthermore, we explore the relevant problems and the possible solutions associated with a retropolation exercise, evidencing that linear models could be the preferred representation for the production of the needed data. The methodology is designed with a focus on economic time series but it could be considered even for other statistical areas. An empirical example is presented: we analyze the back-calculation of Eu15 Industrial Production Index comparing our approach with the Eurostat official one.

Keywords: benchmarking, retropolation, historical reconstruction, back-forecasting, missing past values, aggregation, disaggregation

JEL Classification: C10, C82, C50