Autoregressive Markov switching (ARMS) time series models are used to represent real-world signals whose dynamics may change over time. They have found application in many areas of the natural and social sciences, as well as in engineering. In general, inference in this kind of systems involves two problems: (a) detecting the number of distinct dynamical models that the signal may adopt and (b) estimating any unknown parameters in these models. In this paper, we introduce a class of ARMS time series models that includes many systems resulting from the discretisation of stochastic delay differential equations (DDEs). Remarkably, this class includes cases in which the discretisation time grid is not necessarily aligned with the delays of the DDE, resulting in discrete-time ARMS models with real (non-integer) delays. We describe methods for the maximum likelihood detection of the number of dynamical modes and the estimation of unknown parameters (including the possibly non-integer delays) and illustrate their application with an ARMS model of El Ni\~no--southern oscillation (ENSO) phenomenon.

翻译：自回归马尔可夫切换（ARMS）时间序列模型用于表示动态特性可能随时间变化的真实世界信号，已在自然科学、社会科学及工程领域的诸多场景中得到应用。通常，这类系统的推断涉及两个问题：（a）检测信号可能采用的不同动态模型的数量，以及（b）估计这些模型中的未知参数。本文引入了一类ARMS时间序列模型，该模型涵盖了由随机延迟微分方程（DDE）离散化导出的众多系统。值得注意的是，此类模型包含离散化时间网格不一定与DDE延迟对齐的情形，从而产生具有实数（非整数）延迟的离散时间ARMS模型。我们描述了用于检测动态模式数量及估计未知参数（包括可能为实数的延迟）的最大似然方法，并以厄尔尼诺-南方涛动（ENSO）现象的ARMS模型为例说明其应用。