Asymptotic Forecasting Error Evaluation for Estimated Temporally Aggregated Linear Processes

Abstract

This paper provides implementation details and application examples of the asymptotic error evaluation formulas introduced in the reference [GO14a] concerning three different approaches to the forecasting of linear temporal aggregates using estimated linear processes. The first two techniques are the "all-aggregated" and the "all-disaggregated'' approaches that use either both aggregated data samples and models or their disaggregated counterparts, respectively. The third one is a so called "hybrid" method that consists of carrying out model parameter estimation with data sampled at the highest available frequency and the subsequent prediction with data and models aggregated according to the forecasting horizon of interest. The formulas considered allow to approximately quantify the mean square forecasting errors associated to these three prediction schemes taking into account the estimation error component. We provide explicit details on how to evaluate these formulas and illustrate with several examples how these approximate estimates indicate that the hybrid forecasting scheme tends to outperform the so called "all-aggregated" approach and, in some instances, the "all-disaggregated'' one, that is known to be optimal when model selection and estimation errors are neglected.

Keywords: linear models, ARMA, temporal aggregation, forecasting, finite sample forecasting, multifrequency forecasting, flow temporal aggregation, stock temporal aggregation, multistep forecasting, hybrid forecasting.

JEL Classification: C32, C53