A hidden semi-Markov-switching quantile regression model is introduced as an extension of the Markov-switching one. The proposed allows for arbitrary sojourn-time distributions in states chain. Parameters estimation carried out via maximum likelihood method using Asymmetric Laplace distribution. As a by product specification, formulae and methods forecasting, state prediction, decoding checking...

The score-driven approach to time series modelling is able handle circular data and switching regimes with intra-regime dynamics. Furthermore it enables a dynamic model be fitted linear variable when their joint distribution cylinder. viability of the new method illustrated by estimating models for hourly on wind direction speed in Galicia, north-west Spain. dynamics shown critical importance.