用深度学习动态估计时间序列参数，兼顾模型透明与复杂波动建模。
Neural Network-Based Estimation of Time-Dependent Parameters in AR(p) Processes
- 基于深度学习框架动态估计时变自回归系数，保持可解释性。
- 在高斯与拉普拉斯噪声下均实现准确预测与置信区间构建。
- 适合需要透明建模且处理非平稳数据的研究者或工业场景。
我们研究一种基于简单离散时间动态模型的预测框架，其系数随时间变化。通过深度学习框架恢复模型参数，在保持清晰参数结构的同时，能够捕捉观测现象中的复杂与非平稳模式。分析涵盖两种噪声设定：标准高斯分布及更适用于重尾和剧烈局部波动的拉普拉斯分布。针对两种情形，我们提出了预测方案并分析了不确定性量化，包括预测区间构造。结果表明，结合时变参数估计的简单模型，可在不同噪声假设下成为数学可处理且实际灵活的复杂动态预测工具。一般模型为时变自回归（TVAR(p)），但预测区间公式与数值实验聚焦于TVAR(1)情形。
原文摘要 · Abstract (English)
We investigate a forecasting framework based on a simple discrete-time dynamic model with coefficients varying in time. The parameters of the model are recovered within a deep learning framework, which makes it possible to retain a transparent parametric structure while simultaneously accounting for complex and nonstationary patterns in the observed phenomenon. Our analysis covers two specifications of the noise process. Besides the standard Gaussian setting, we also consider Laplace-distributed noise, which can offer a more adequate description in the presence of heavier tails and sharper local fluctuations. For both cases, we formulate the predictive scheme of the model and analyze the associated uncertainty quantification, including the construction of prediction intervals. The results illustrate that a relatively simple model, when combined with time-dependent parameter estimation, can serve as a mathematically tractable and practically flexible tool for forecasting complex dynamics under different noise assumptions. The general model is stated for TVAR($p$), while the prediction-interval formulas and the numerical experiments are developed for the TVAR(1) case.
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