Modern time series data often display complex nonlinear dependencies along with irregular regime-switching behaviors. These features present technical challenges in modeling, inference, and in offering insightful understanding into the underlying stochastic phenomena. To tackle these challenges, we introduce a novel modeling framework known as the Deep Switching State Space Model (DS$^3$M). This framework is engineered to make accurate forecasts for such time series while adeptly identifying the irregular regimes hidden within the dynamics. These identifications not only have significant economic ramifications but also contribute to a deeper understanding of the underlying phenomena. In DS$^3$M, the architecture employs discrete latent variables to represent regimes and continuous latent variables to account for random driving factors. By melding a Recurrent Neural Network (RNN) with a nonlinear Switching State Space Model (SSSM), we manage to capture the nonlinear dependencies and irregular regime-switching behaviors, governed by a Markov chain and parameterized using multilayer perceptrons. We validate the effectiveness and regime identification capabilities of DS$^3$M through short- and long-term forecasting tests on a wide array of simulated and real-world datasets, spanning sectors such as healthcare, economics, traffic, meteorology, and energy. Experimental results reveal that DS$^3$M outperforms several state-of-the-art models in terms of forecasting accuracy, while providing meaningful regime identifications.

翻译：现代时间序列数据常呈现复杂的非线性依赖关系与不规则机制转换行为。这些特征给建模、推断以及理解潜在随机现象带来技术挑战。为应对这些挑战，我们提出一种名为深度切换状态空间模型（DS$^3$M）的新型建模框架。该框架专为准确预测此类时间序列而设计，同时能有效识别动态过程中隐藏的不规则机制。这些识别不仅具有重要的经济学意义，更有助于深入理解潜在现象。在DS$^3$M中，架构采用离散潜变量表示机制，连续潜变量刻画随机驱动因素。通过融合递归神经网络（RNN）与非线性切换状态空间模型（SSSM），我们成功捕捉了由马尔可夫链控制、多层感知机参数化的非线性依赖关系与不规则机制转换行为。我们通过在涵盖医疗、经济、交通、气象和能源等领域的合成数据集与真实数据集上进行短期与长期预测测试，验证了DS$^3$M的有效性及机制识别能力。实验结果表明，DS$^3$M在预测精度上优于多个现有最优模型，同时能提供有意义的机制识别结果。