Abstract: This paper addresses the nonlinear and non-stationary characteristics of automotive sales time series by proposing a Levenberg-Marquardt (LM)-based method for the back propagation (BP) neural network prediction model. Using a company's car sales data spanning 45 consecutive weeks as the research subject, a sliding window technique is applied to construct sample pairs with 5- dimensional inputs and 1-dimensional outputs. Min-Max normalization is used to eliminate dimensional impacts, and a three-layer BP network structure (5-8-1) is designed and implemented via MATLAB 7.0 for model training. Experimental results show that the model achieved the target error, the mean squared error is 5.07659e-007 in the 31st iteration. The test set's mean absolute percentage error (MAPE) is only 0.05%, with absolute prediction errors consistently below 0.6 vehicles. This significantly outperforms similar multivariate long short-term memory (LSTM) prediction models (MAPE=3.73%) and system dynamics (SD) prediction models (MAPE=0.22% to 1.83%). The model effectively captures the intrinsic patterns of sales sequences, providing high- precision decision-making support for corporate production planning, inventory management, and marketing strategy formulation.

Key words: BP neural network; time series forecasting; automobile sales; MATLAB; sliding window

摘要： 文章针对汽车销售量时间序列的非线性、非平稳特性，提出一种基于莱文贝格-马夸特 （LM）算法优化的反向传播（BP）神经网络预测模型。以某公司连续 45 周汽车销售量数据 为研究对象，采用滑动窗口技术构建 5 维输入-1 维输出的样本对，通过 Min-Max 归一化消除 量纲影响，设计 5-8-1 三层 BP 网络结构并利用 MATLAB 7.0 实现模型训练。实验结果表明： 模型在第 31 轮迭代达到目标误差，即均方误差（MSE）值为 5.07659e-007，测试集平均绝对 百分比误差（MAPE）仅为 0.05%，预测误差绝对值均小于 0.6 辆，显著优于多变量长短期记 忆（LSTM）类似预测模型（MAPE=3.73%）和系统动力学（SD）类似预测模型（MAPE=0.22% 至 1.83%）。该模型能有效捕捉销售量序列的内在规律，可为企业生产计划、库存管理及营销 策略制定提供高精度决策依据。

关键词: BP 神经网络；时间序列预测；汽车销售量；MATLAB；滑动窗口