Non-negative autoregressive moving average models for intermittent demand: Forecast accuracy and inventory implications
针对ARMA模型对间歇性需求可能产生负预测值的问题，提出非负ARMA模型，在沃尔玛和化妆品零售商数据上验证了其预测精度和库存效率均优于标准基准。
Autoregressive moving average (ARMA) models are widely used in retail demand forecasting, particularly for stationary data. However, their performance on Walmart’s demand data in the M5 competition has been low. One reason could be that ARMA models can generate negative forecasts for intermittent demand patterns, which are prevalent in the Walmart dataset used in the M5 competition. To address this limitation, we propose a novel approach that enables ARMA models to effectively forecast intermittent demand. Specifically, we establish conditions under which a generic ARMA model generates non-negative filters and forecasts. Additionally, we derive expressions for approximate prediction intervals, making the approach suitable for stock control applications. Through an empirical analysis of 42,686 time series from Walmart’s M5 competition data and 24,029 series from a global cosmetics retailer, we show that a simple non-negative ARMA(1,1) model significantly outperforms standard benchmarks in both point forecasts and prediction intervals. Moreover, the empirical inventory performance analysis shows that the non-negative ARMA(1,1) leads to the highest inventory efficiency as compared to all the benchmarks considered in the paper. These findings underscore the potential of ARMA models to effectively forecast intermittent demand when non-negativity is enforced.