Abstract Demand forecasting is of major importance for manufacturing companies since it provides a basis for production planning. However, demand forecasting can be a difficult task because customer demands often fluctuate due to several influences. Methods of nonlinear dynamics have shown promising results in numerous applications but they have mostly been neglected in the context of demand forecasting. This paper evaluates the forecasting performance of local k -nearest neighbor models, which base on the theory of dynamical systems, in a comprehensive empirical study utilizing a large dataset of industrial time series of the M3-Competition. After a broad literature review, the theoretical background is described. Subsequently, different parameter configurations and model selection strategies are compared. A locally constant mean and a locally constant median are compared to locally linear regression models with four different regularization methods and different parameter configurations. In this comparison, the locally constant mean and the locally linear ridge regression with high regularization parameters provide the best trade-offs between forecast accuracy and computation times. Finally, these models achieve a high performance regarding low forecast errors, short computation times as well as high service levels in an inventory simulation compared to established benchmark methods. In particular, they obtain the best results among all applied methods regarding short time series. Moreover, they achieve the lowest errors considering the original accuracy criterion of the M3-Competition. Hence, local k -nearest neighbor models can be regarded as a valid alternative for demand forecasting in an industrial context, accomplishing high forecast accuracy with short computation times.

中文翻译：

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通过局部k-最近邻模型预测客户对生产计划的需求

摘要 需求预测对制造企业非常重要，因为它为生产计划提供了基础。然而，需求预测可能是一项艰巨的任务，因为客户需求通常会因多种影响而波动。非线性动力学方法已在众多应用中显示出有希望的结果，但它们在需求预测的背景下大多被忽视。本文利用 M3-Competition 的工业时间序列的大型数据集，在综合实证研究中评估了基于动力系统理论的局部 k 最近邻模型的预测性能。在广泛查阅文献后，描述了理论背景。随后，比较了不同的参数配置和模型选择策略。将局部常数均值和局部常数中位数与具有四种不同正则化方法和不同参数配置的局部线性回归模型进行比较。在这个比较中，局部常数均值和具有高正则化参数的局部线性岭回归提供了预测精度和计算时间之间的最佳权衡。最后，与既定的基准方法相比，这些模型在库存模拟中实现了低预测误差、短计算时间以及高服务水平方面的高性能。特别是，它们在关于短时间序列的所有应用方法中获得了最好的结果。此外，考虑到 M3-Competition 的原始精度标准，它们实现了最低的误差。因此，