Demand forecasting by temporal aggregation

Abstract

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.

Forecasting with temporal hierarchies

“…Souza and Smith (2004) use simulations to find that for ARFIMA(p, d, q) processes with d < 0, forecasts from the aggregated series are generally superior than aggregated forecasts from the disaggregate series, while the results are reversed for d > 0 but the evidence is not as clear. Rostami-Tabar et al (2013) look into identifying an optimal aggregation level when the disaggregate process is either MA(1) or AR(1) and find that in general the higher the aggregation the lower the forecast errors are, when forecasting by single exponential smoothing. For more complex processes Nikolopoulos et al (2011) demonstrate that forecasting accuracy does not change monotonically as the aggregation level increases.…”

Forecasting With Temporally Aggregated Demand Signals in a Retail Supply Chain

“…; Rostami‐Tabar et al. ) dimensions. We present in Table an overview of the risk‐pooling literature in SCM research.…”

Supply chain forecasting: Theory, practice, their gap and the future

“…ADIDA has been found effectively to operate as a forecasting method ''self-improving'' mechanism; changing the data series features through frequency transformation may help extrapolation methods achieve better accuracy performance. Building on those empirical results, some theoretical analysis was presented for data following an AR(1) and MA(1) process by Rostami-Tabar et al (2013) and a more general ARMA(1,1) process by Rostami-Tabar et al (2014). This analysis led to theoretically determined optimum aggregation levels for the ADIDA framework (as opposed to the empirically determined optimum levels of aggregation suggested by Nikolopoulos et al, 2011) under specific demand generation processes).…”