Hybrid Forecasting with Estimated Temporally Aggregated Linear Processes

Abstract

We introduce a new strategy for the prediction of linear temporal aggregates; we call it ‘hybrid’ and study its performance using asymptotic theory. This scheme 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. We develop explicit expressions that approximately quantify the mean square forecasting errors associated with the different prediction schemes and that take into account the estimation error component. 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’ strategy that is known to be optimal when model selection and estimation errors are neglected. Unlike other related approximate formulas existing in the literature, those proposed in this paper are totally explicit and require neither assumptions on the second-order stationarity of the sample nor Monte Carlo simulations for their evaluation.