Papers › Partially Hidden Markov Chain Linear Autoregressive model: inference and forecasting
Partially Hidden Markov Chain Linear Autoregressive model: inference and forecasting
Fatoumata Dama, Christine Sinoquet
Time series subject to change in regime have attracted much interest in domains such as econometry, finance or meteorology. For discrete-valued regimes, some models such as the popular Hidden Markov Chain (HMC) describe time series whose state process is unknown at all time-steps. Sometimes, time series are firstly labelled thanks to some annotation function. Thus, another category of models handles the case with regimes observed at all time-steps. We present a novel model which addresses the intermediate case: (i) state processes associated to such time series are modelled by Partially Hidden Markov Chains (PHMCs); (ii) a linear autoregressive (LAR) model drives the dynamics of the time series, within each regime. We describe a variant of the expection maximization (EM) algorithm devoted to PHMC-LAR model learning. We propose a hidden state inference procedure and a forecasting function that take into account the observed states when existing. We assess inference and prediction performances, and analyze EM convergence times for the new model, using simulated data. We show the benefits of using partially observed states to decrease EM convergence times. A fully labelled scheme with unreliable labels also speeds up EM. This offers promising prospects to enhance PHMC-LAR model selection. We also point out the robustness of PHMC-LAR to labelling errors in inference task, when large training datasets and moderate labelling error rates are considered. Finally, we highlight the remarkable robustness to error labelling in the prediction task, over the whole range of error rates.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Tasks
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections