Multistep quantile forecasts for supply chain and logistics operations: bootstrapping, the GARCH model and quantile regression based approaches

In this paper, we discuss and compare empirically various ways of computing multistep quantile forecasts of demand, with a special emphasis on the use of the quantile regression methodology. Such forecasts constitute a basis for production planning and inventory management in logistics systems optimized according to the cycle service level approach. Different econometric methods and models are considered: direct and iterated computations, linear and nonlinear (GARCH) models, simulation and non-simulation based procedures and parametric as well as semiparametric specifications. These methods are applied to compute multiperiod quantile forecasts of the monthly microeconomic time series from the popular M3 competition database. According to various accuracy measures for quantile predictions, the best procedures are based on simulation techniques using predictive distributions generated by either the quantile regression methodology combined with random draws from the uniform distribution or parametric and nonparametric bootstrap techniques. These methods lead to large reductions in the total costs of logistics systems as compared with non-simulation based procedures. For example, in the case of forecasting 12 months ahead, relatively short time series and a high cycle service level, the quantile regression based simulation approach reduces the average supply chain cost per unit of output by about 70–85%. At the shortest horizons, the GARCH model should be seriously considered among the preferred forecasting solutions for production and inventory planning.