Quantile smoothing in supply chain and logistics forecasting

Abstract

In this paper, we re-examine the exponential smoothing model in the context of its use in supply chain and logistics forecasting when supply chain or logistics costs are measured by the doubly linear (LINLIN) loss function of errors of demand forecasts. The parameters of our models are optimized with respect to the LINLIN loss, i.e., by applying the quantile regression estimator. The resulting forecasting procedures, which we call quantile smoothing, are then used to forecast the monthly microeconomic time series and the quarterly and annual sales data from the M3 forecast competition. According to accuracy measures for quantile predictions and in part also statistical tests of the forecasting results, the suggested procedures lead to better quantile forecasts than both standard econometric approaches and popular methods from the practice of logistics forecasting in the case of the longer among the microeconomic monthly data. On the contrary, for the other time series, the best outcomes are usually obtained through a simple modeling of the conditional median or mean, although quantile smoothing still remains among the best forecasting procedures. Moreover, the best performing quantile smoothing equation changes across quantiles.