We propose an extension of Markov-switching generalized additive models for location, scale, and shape (MS-GAMLSS) that allows covariates to influence not only the parameters of the state-dependent distributions but also the state transition probabilities. Traditional MS-GAMLSS, which combine distributional regression with hidden Markov models, typically assume time-homogeneous (i.e., constant) transition probabilities, thereby preventing regime shifts from responding to covariate-driven changes. Our approach overcomes this limitation by modeling the transition probabilities as smooth functions of covariates, enabling a flexible, data-driven characterization of covariate-dependent regime dynamics. Estimation is carried out within a penalized likelihood framework, where automatic smoothness selection controls model complexity and guards against overfitting. We evaluate the proposed methodology through simulations and applications to daily Lufthansa stock prices and Spanish energy prices. Our results show that incorporating macroeconomic indicators into the transition probabilities yields additional insights into market dynamics. Data and R code to reproduce the results are available online.

翻译：我们提出了一种针对位置、尺度与形状的马尔可夫切换广义可加模型（MS-GAMLSS）的扩展形式，该扩展允许协变量不仅影响状态依赖分布的参数，还能影响状态转移概率。传统的MS-GAMLSS将分布回归与隐马尔可夫模型相结合，通常假设转移概率具有时间齐性（即恒定不变），从而阻碍了体制转换对协变量驱动变化的响应。我们的方法通过将转移概率建模为协变量的平滑函数来克服这一局限，实现了对协变量依赖型体制动态的灵活、数据驱动的刻画。估计在惩罚似然框架内进行，其中自动平滑度选择机制可控制模型复杂度并防止过拟合。我们通过模拟实验，并应用于汉莎航空日股价与西班牙能源价格数据，对所提方法进行了评估。结果表明，将宏观经济指标纳入转移概率能为市场动态提供更多洞见。重现结果所需的数据与R代码已在线公开。