The Hidden Markov Model (HMM) can predict the future value of a time series based on its current and previous values, making it a powerful algorithm for handling various types of time series. Numerous studies have explored the improvement of HMM using advanced techniques, leading to the development of several variations of HMM. Despite these studies indicating the increased competitiveness of HMM compared to other advanced algorithms, few have recognized the significance and impact of incorporating multistep stochastic states into its performance. In this work, we propose a Pyramidal Hidden Markov Model (PHMM) that can capture multiple multistep stochastic states. Initially, a multistep HMM is designed for extracting short multistep stochastic states. Next, a novel time series forecasting structure is proposed based on PHMM, which utilizes pyramid-like stacking to adaptively identify long multistep stochastic states. By employing these two schemes, our model can effectively handle non-stationary and noisy data, while also establishing long-term dependencies for more accurate and comprehensive forecasting. The experimental results on diverse multivariate time series datasets convincingly demonstrate the superior performance of our proposed PHMM compared to its competitive peers in time series forecasting.

翻译：隐马尔可夫模型（HMM）能够基于时间序列的当前及历史值预测未来取值，是处理各类时间序列的强大算法。众多研究探索了利用先进技术改进HMM的方法，衍生出多种HMM变体。尽管这些研究表明HMM相较于其他高级算法的竞争力有所提升，但鲜有研究认识到引入多步随机状态对其性能的重要性和影响。本文提出一种金字塔隐马尔可夫模型（PHMM），该模型能够捕获多组多步随机状态。首先设计多步HMM以提取短程多步随机状态，随后基于PHMM构建新型时间序列预测框架，通过金字塔式堆叠自适应识别长程多步随机状态。通过这两种机制，本模型既能有效处理非平稳与噪声数据，又能建立长期依赖关系以实现更精准全面的预测。在多个多变量时间序列数据集上的实验结果令人信服地表明，所提出的PHMM在时间序列预测任务中性能显著优于对比算法。