Markov-switching generalized additive models

TL;DR

This paper introduces a flexible class of Markov-switching generalized additive models that nonparametrically estimate covariate effects in regime-switching time series, extending existing models with a penalized likelihood approach.

Contribution

It develops a novel framework combining Markov-switching models with nonparametric additive regression, enabling more flexible modeling of regime-dependent relationships.

Findings

The proposed method is feasible and effective as shown by simulations.

Application to energy prices demonstrates practical utility.

Model encompasses parametric and nonparametric regression models.

Abstract

We consider Markov-switching regression models, i.e. models for time series regression analyses where the functional relationship between covariates and response is subject to regime switching controlled by an unobservable Markov chain. Building on the powerful hidden Markov model machinery and the methods for penalized B-splines routinely used in regression analyses, we develop a framework for nonparametrically estimating the functional form of the effect of the covariates in such a regression model, assuming an additive structure of the predictor. The resulting class of Markov-switching generalized additive models is immensely flexible, and contains as special cases the common parametric Markov-switching regression models and also generalized additive and generalized linear models. The feasibility of the suggested maximum penalized likelihood approach is demonstrated by simulation and further illustrated by modelling how energy price in Spain depends on the Euro/Dollar exchange rate.