Markov switching regression processes belong to the class of Hidden Markov models (HMMs). They provide a higher flexibility than, for example, simple (auto)regression. The main reason for their popularity is the convenient interpretability. For sufficiently long time series, the different regimes can be associated with abrupt macroeconomic events (war, changing governmental policy,etc.). However, it is not always intuitively clear why the regime switching follows a Markov law. Hidden semi-Markov models (HSMMs) are an extension of HMMs. The most appealing property of a HSMM lies in the flexibility of the runlength distributions which are given explicitly instead of implicitly following the geometric distributions of a HMM. We present a generalization of the Markov regime switching framework and introduce the semi-Markov switching (auto)regressive processes. In particular, we focus on the theory for right-censored HSMMs introduced by Guédon in 2003. We present an EM algorithm for auto(regression) models with different state occupancy distributions. Subsequently, we investigate a modified, computational convenient M-step in terms of the One-Step-Late. Finally, the performance of the estimation procedure is analyzed using an economic data set
