Financial markets exhibit alternating periods of rising and falling prices. Stock traders seeking to make profitable investment decisions have to account for those trends, where the goal is to accurately predict switches from bullish to bearish markets and vice versa. Popular tools for modelling financial time series are hidden Markov models, where a latent state process is used to explicitly model switches among different market regimes. In their basic form, however, hidden Markov models are not capable of capturing both short- and long-term trends, which can lead to a misinterpretation of short-term price fluctuations as changes in the long-term trend. In this article, we demonstrate how hierarchical hidden Markov models can be used to draw a comprehensive picture of market behaviour, which can contribute to the development of more sophisticated trading strategies. The feasibility of the suggested approach is illustrated in two real-data applications, where we model data from the Deutscher Aktienindex and the Deutsche Bank stock. The proposed methodology is implemented in the R package fHMM, which is available on CRAN.

金融市场表现出价格上涨和下跌的交替时期。寻求做出有利可图的投资决策的股票交易者必须考虑这些趋势，其目标是准确预测从看涨市场到看跌市场的转变，反之亦然。金融时间序列建模的流行工具是隐马尔可夫模型，其中潜在状态过程用于显式建模不同市场机制之间的转换。然而，在其基本形式中，隐马尔可夫模型不能同时捕捉短期和长期趋势，这可能导致将短期价格波动误解为长期趋势的变化。在本文中，我们展示了如何使用分层隐马尔可夫模型来全面描绘市场行为，这有助于开发更复杂的交易策略。建议方法的可行性在两个真实数据应用程序中得到了说明，我们对来自 Deutscher Aktienindex 和德意志银行股票的数据进行建模。所提出的方法在 R 包 fHMM 中实现，该包可在 CRAN 上使用。