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.

翻译：自回归（AR）模型因其可解释性在时间序列分析中仍被广泛使用，但传统参数估计方法计算成本高且易出现收敛问题。本文通过将自回归结构直接嵌入前馈神经网络，提出一种神经网络（NN）形式的AR估计方法，使其既能通过反向传播实现系数估计，又保持可解释性。在125,000个具有短期依赖性的合成AR(p)时间序列（1 ≤ p ≤ 5）上的仿真实验表明，所提出的基于神经网络的方法能持续恢复所有序列的模型系数，而条件最大似然（CML）方法在大约55%的情况下未能收敛。当两种方法均收敛时，估计精度相当，相对误差、R²和困惑度/似然性差异可忽略不计。然而，当CML方法失效时，基于神经网络的方法仍能提供可靠估计。在所有情况下，神经网络估计器均实现显著计算加速，中位数加速比达12.6倍，对于高阶模型更可达34.2倍。总体结果表明，梯度下降神经网络优化可为可解释AR参数估计提供快速高效的替代方案。