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 Grigoryeva and Ortega (2014a) 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 illustrate these developments with several examples.