Forecasting aggregate demand: Analytical comparison of top-down and bottom-up approaches in a multivariate exponential smoothing framework

Forecasting aggregate demand represents a crucial aspect in all industrial sectors. In this paper, we provide the analytical prediction properties of top-down (TD) and bottom-up (BU) approaches when forecasting the aggregate demand using a multivariate exponential smoothing as demand planning framework. We extend and generalize the results achieved by Widiarta et al. (2009) by employing an unrestricted multivariate framework allowing for interdependency between its variables. Moreover, we establish the necessary and sufficient condition for the equality of mean squared errors (MSEs) of the two approaches. We show that the condition for the equality of MSEs holds even when the moving average parameters of the individual components are not identical. In addition, we show that the relative forecasting accuracy of TD and BU depends on the parametric structure of the underlying framework. Simulation results confirm our theoretical findings. Indeed, the ranking of TD and BU forecasts is led by the parametric structure of the underlying data generation process, regardless of possible misspecification issues.