用神经网络反向传播加速自回归模型参数估计，又快又准还可解释。
Fast and Interpretable Autoregressive Estimation with Neural Network Backpropagation
- 把自回归结构嵌入前馈网络，用反向传播直接算系数。
- 12.5万组模拟数据中，95%以上成功收敛，比传统方法提升近一倍。
- 适合需要快速可解释时间序列建模的研究者或工程应用。
自回归（AR）模型因其可解释性在时间序列分析中广泛应用，但传统参数估计方法计算成本高且易出现收敛问题。本文提出一种将自回归结构直接嵌入前馈神经网络的神经网络（NN）形式化方法，通过反向传播实现系数估计，同时保持可解释性。在12.5万组具有短期依赖（1 ≤ p ≤ 5）的合成AR(p)时间序列上进行仿真实验，结果表明：所提方法在所有情况下均能稳定恢复模型系数，而条件最大似然（CML）在约55%的情况下无法收敛；当两者均收敛时，估计精度相当，相对误差、R²及困惑度/似然值差异可忽略；而在CML失败时，该方法仍能提供可靠估计。整体上，该方法实现显著计算提速，中位速度提升达12.6倍，高阶模型下最高可达34.2倍。结果表明，基于梯度下降的神经网络优化可为可解释的自回归参数估计提供高效替代方案。
原文摘要 · Abstract (English)
Autoregressive (AR) models remain widely used in time series analysis due to their interpretability, but convencional parameter estimation methods can be computationally expensive and prone to convergence issues. This paper proposes a Neural Network (NN) formulation of AR estimation by embedding the autoregressive structure directly into a feedforward NN, enabling coefficient estimation through backpropagation while preserving interpretability. Simulation experiments on 125,000 synthetic AR(p) time series with short-term dependence (1 <= p <= 5) show that the proposed NN-based method consistently recovers model coefficients for all series, while Conditional Maximum Likelihood (CML) fails to converge in approximately 55% of cases. When both methods converge, estimation accuracy is comparable with negligible differences in relative error, R2 and, perplexity/likelihood. However, when CML fails, the NN-based approach still provides reliable estimates. In all cases, the NN estimator achieves substantial computational gains, reaching a median speedup of 12.6x and up to 34.2x for higher model orders. Overall, results demonstrate that gradient-descent NN optimization can provide a fast and efficient alternative for interpretable AR parameter estimation.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。