  We propose a novel class of flexible latent-state time series regression
models which we call Markov-switching generalized additive models for location,
scale and shape. In contrast to conventional Markov-switching regression
models, the presented methodology allows us 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. We propose an estimation approach
based on the EM algorithm, where we use the gradient boosting framework 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 setting, where we model the conditional distribution
of the daily average price of energy in Spain over time.
