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Hybrid Forecasting with Estimated Temporally Aggregated Linear Processes

Forthcoming, Journal of Forecasting

20 Pages Posted: 19 Sep 2012 Last revised: 2 Jun 2014

Lyudmila Grigoryeva

University of Konstanz

Juan-Pablo Ortega

Universität Sankt Gallen; Centre National de la Recherche Scientifique (CNRS)

Date Written: September 19, 2012


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 to 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, the ones 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.

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

JEL Classification: C32, C53

Suggested Citation

Grigoryeva, Lyudmila and Ortega, Juan-Pablo, Hybrid Forecasting with Estimated Temporally Aggregated Linear Processes (September 19, 2012). To appear in the Journal of Forecasting; Forthcoming, Journal of Forecasting. Available at SSRN: or

Lyudmila Grigoryeva (Contact Author)

University of Konstanz ( email )

Fach D-144
Universitätsstraße 10
Konstanz, D-78457

Juan-Pablo Ortega

Universität Sankt Gallen ( email )

Bodanstrasse 6
St. Gallen, St. Gallen CH-9000


Centre National de la Recherche Scientifique (CNRS) ( email )

16 route de Gray
Besançon, 25030


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