A turbidity time series, recorded every 15 min in a first-order Scottish stream for more than a year, along with two covariates (stage height and rainfall), is considered. Turbidity time series have complex dynamics because they are nonlinear, nonnormal, nonstationary, with a long memory, and present missing values. Given these issues the turbidity process is analyzed by Markov switching autoregressive models under the Bayesian paradigm. Since the multimodality of the posterior density novel evolutionary Monte Carlo (EMC) algorithms incorporating a few original features are developed to better traverse the posterior surface and escape from local basins of attraction. This because a population of chains are processed in parallel exchanging information one another and with different temperatures attached to each chain. These advanced EMC algorithms allow performing both Bayesian inference and model choice. Hence, it is possible to efficiently fit the actual data, reconstruct the sequence of hidden states, restore the missing values, and classify the observations into a few regimes, providing new insight on turbidity dynamics. A comparison with different nonlinear time series models is also proposed. Finally, a simulation study on the selection of the tuning factors of the EMC algorithm is presented.

中文翻译：

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一种通过马尔可夫切换自回归模型分析浊度高频时间序列的进化蒙特卡罗方法

考虑了一年多时间在苏格兰一级河流中每 15 分钟记录一次的浊度时间序列，以及两个协变量（阶段高度和降雨量）。浊度时间序列具有复杂的动态特性，因为它们是非线性的、非正态的、非平稳的、具有长记忆力并存在缺失值。鉴于这些问题，在贝叶斯范式下通过马尔可夫切换自回归模型来分析浊度过程。由于后密度新进化蒙特卡罗 (EMC) 算法的多模态结合了一些原始特征，因此可以更好地遍历后表面并逃离局部吸引力盆地。这是因为一组链是并行处理的，彼此交换信息，并且每个链具有不同的温度。这些高级 EMC 算法允许执行贝叶斯推理和模型选择。因此，可以有效地拟合实际数据，重建隐藏状态序列，恢复缺失值，并将观察结果分类为几个区域，为浊度动力学提供新的见解。还提出了与不同非线性时间序列模型的比较。最后，对EMC算法的调谐因子的选择进行了仿真研究。