Finite sample forecasting with estimated temporally aggregated linear processes

TL;DR

This paper introduces a finite sample predictor for linear time series models that accounts for estimation error without requiring stationarity assumptions, and proposes a hybrid forecasting scheme that can outperform traditional methods.

Contribution

It provides a new finite sample forecasting formula that incorporates estimation error without stationarity assumptions and introduces a hybrid scheme for temporal aggregation forecasting.

Findings

The proposed predictor accurately accounts for estimation error.

The hybrid scheme can outperform the all-disaggregated approach.

Formulas do not require second order stationarity or Monte Carlo simulations.

Abstract

We propose a finite sample based predictor for estimated linear one dimensional time series models and compute the associated total forecasting error. The expression for the error that we present takes into account the estimation error. Unlike existing solutions in the literature, our formulas require neither assumptions on the second order stationarity of the sample nor Monte Carlo simulations for their evaluation. This result is used to prove the pertinence of a new hybrid scheme that we put forward for the forecast of linear temporal aggregates. This novel strategy consists of carrying out the parameter estimation based on disaggregated data and the prediction based on the corresponding aggregated model and data. We show that in some instances this scheme has a better performance than the "all-disaggregated" approach presented as optimal in the literature.