Gradient boosting in Markov-switching generalized additive models for location, scale, and shape

Abstract 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.