Markov-switching generalized additive models for location, scale, and shape constitute a novel class of flexible latent-state time series regression models. In contrast to conventional Markov-switching regression models, they can be used to model different state-dependent parameters of the response distribution — not only the mean, but also variance, skewness, and kurtosis parameters — as potentially smooth functions of a given set of explanatory variables. In addition, the set of possible distributions that can be specified for the response is not limited to the exponential family but additionally includes, for instance, a variety of Box-Cox-transformed, zero-inflated, and mixture distributions. An estimation approach based on the EM algorithm is proposed, where the gradient boosting framework is exploited to prevent overfitting while simultaneously performing variable selection. The feasibility of the suggested approach is assessed in simulation experiments and illustrated in a real-data application, where the conditional distribution of the daily average price of energy in Spain is modeled over time.

用于位置、尺度和形状的马尔可夫切换广义加性模型构成了一类新的灵活的潜在状态时间序列回归模型。与传统的马尔可夫切换回归模型相比，它们可用于对响应分布的不同状态相关参数进行建模——不仅是均值，还有方差、偏度和峰度参数——作为给定集合的潜在平滑函数解释变量。此外，可以为响应指定的可能分布集不限于指数族，还包括例如各种 Box-Cox 变换、零膨胀和混合分布。提出了一种基于EM算法的估计方法，其中梯度提升框架用于防止过度拟合，同时执行变量选择。建议方法的可行性在模拟实验中进行了评估，并在真实数据应用程序中进行了说明，其中西班牙每日平均能源价格的条件分布随时间建模。