Abstract
Intermittency are a common and challenging problem in demand forecasting. We introduce a new, unified framework for building probabilistic forecasting models for intermittent demand time series, which incorporates and allows to generalize existing methods in several directions. Our framework is based on extensions of well-established model-based methods to discrete-time renewal processes, which can parsimoniously account for patterns such as aging, clustering and quasi-periodicity in demand arrivals. The connection to discrete-time renewal processes allows not only for a principled extension of Croston-type models, but additionally for a natural inclusion of neural network based models—by replacing exponential smoothing with a recurrent neural network. We also demonstrate that modeling continuous-time demand arrivals, i.e., with a temporal point process, is possible via a trivial extension of our framework. This leads to more flexible modeling in scenarios where data of individual purchase orders are directly available with granular timestamps. Complementing this theoretical advancement, we demonstrate the efficacy of our framework for forecasting practice via an extensive empirical study on standard intermittent demand data sets, in which we report predictive accuracy in a variety of scenarios.
Highlights
Intermittent demand forecasting (IDF) is concerned with demand data where demand appears sporadically in time [1,2,3,4], i.e., long runs of zero demand are observed before periods with nonzero demand
On the M5 data set where hyperparameters were optimized, we find that Recurrent neural networks (RNN) significantly outperform all other model-based methods in both probabilistic and point forecast performance, and are slightly better than point forecast methods as measured by root mean squared error (RMSE) and root mean squared scaled error (RMSSE)
IDF is a uniquely challenging problem; the definition of good forecasts is as elusive as the techniques used to produce them
Summary
Intermittent demand forecasting (IDF) is concerned with demand data where demand appears sporadically in time [1,2,3,4], i.e., long runs of zero demand are observed before periods with nonzero demand. We draw previously unrecognized connections between existing IDF models and renewal processes We note that these two subjects of applied statistics both deal with temporal sparsity and have been developed for planning spare parts inventories. We introduce a flexible set of discrete-time renewal process models for stationary intermittent demand. We illustrate that these models are able to capture patterns such as temporal clustering, aging, and quasi-periodicity of demand.
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