Time series subject to change in regime have attracted much interest in\ndomains such as econometry, finance or meteorology. For discrete-valued\nregimes, some models such as the popular Hidden Markov Chain (HMC) describe\ntime series whose state process is unknown at all time-steps. Sometimes, time\nseries are firstly labelled thanks to some annotation function. Thus, another\ncategory of models handles the case with regimes observed at all time-steps. We\npresent a novel model which addresses the intermediate case: (i) state\nprocesses associated to such time series are modelled by Partially Hidden\nMarkov Chains (PHMCs); (ii) a linear autoregressive (LAR) model drives the\ndynamics of the time series, within each regime. We describe a variant of the\nexpection maximization (EM) algorithm devoted to PHMC-LAR model learning. We\npropose a hidden state inference procedure and a forecasting function that take\ninto account the observed states when existing. We assess inference and\nprediction performances, and analyze EM convergence times for the new model,\nusing simulated data. We show the benefits of using partially observed states\nto decrease EM convergence times. A fully labelled scheme with unreliable\nlabels also speeds up EM. This offers promising prospects to enhance PHMC-LAR\nmodel selection. We also point out the robustness of PHMC-LAR to labelling\nerrors in inference task, when large training datasets and moderate labelling\nerror rates are considered. Finally, we highlight the remarkable robustness to\nerror labelling in the prediction task, over the whole range of error rates.\n