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Demand forecasting performance is subject to the uncertainty underlying the time series an organisation is dealing with. There are many approaches that may be used to reduce uncertainty and thus to improve forecasting performance. One intuitively appealing such approach is to aggregate demand in lowerfrequency 'time buckets'. The approach under concern is termed to as Temporal Aggregation and in this paper we investigate its impact on forecasting performance. We assume that the non-aggregated demand follows either a moving average process of order one or a first-order autoregressive process and a Single Exponential Smoothing (SES) procedure is used to forecast demand. These demand processes are often encountered in practice and SES is one of the standard estimators used in industry. Theoretical Mean Squared Error expressions are derived for the aggregated and non-aggregated demand in order to contrast the relevant forecasting performances. The theoretical analysis is supported by an extensive numerical investigation and experimentation with an empirical dataset. The results indicate that performance improvements achieved through the aggregation approach are a function of the aggregation level, the smoothing constant and the process parameters. Valuable insights are offered to practitioners and the paper closes with an agenda for further research in this area.

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Recent advances have demonstrated the benefits of temporal aggregation for demand forecasting, including increased accuracy, improved stock control and reduced modelling uncertainty. With temporal aggregation a series is transformed, strengthening or attenuating different elements and thereby enabling better identification of the time series structure. Two different

Earlier research on the effects of non-overlapping temporal aggregation on demand forecasting 5 showed the benefits associated with such an approach under a stationary AR(1) or MA(1) processes for decision 6 making conducted at the disaggregate level. The first objective of this note is to extend those important results by 7 considering a more general underlying demand process. The second objective is to assess the conditions under 8 which aggregation may be a preferable approach for improving decision making at the aggregate level as well. 9We confirm the validity of previous results under more general conditions and we show the increased benefit 10 resulting from forecasting by temporal aggregation at lower frequency time units. 11 12

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Abstract:In this paper the relative effectiveness of top-down (TD) versus bottom-up (BU) approaches is compared for cross-sectionally forecasting aggregate and sub-aggregate demand. We assume that the sub-aggregate demand follows a non-stationary Integrated Moving Average (IMA) process of order one and a Single Exponential Smoothing (SES) procedure is used to extrapolate future requirements. Such demand processes are often encountered in practice and SES is one of the standard estimators used in industry (in addition to being the optimal estimator for an IMA process). Theoretical variances of forecast error are derived for the BU and TD approach in order to contrast the relevant forecasting performances. The theoretical analysis is supported by an extensive numerical investigation at both the aggregate and subaggregate level, in addition to empirically validating our findings on a real dataset from a European superstore. The results demonstrate the increased benefit resulting from crosssectional forecasting in a non-stationary environment than in a stationary one. Valuable insights are offered to demand planners and the paper closes with an agenda for further research in this area. 2