Bayesian multivariate semi-Markov-switching mixed data sampling

We introduce a flexible model for multivariate time-series exhibiting heterogeneous sampling frequencies, where time-varying unobservable heterogeneity is captured by a finite number of latent regimes. The latent unobservable process evolves over time according to a semi-Markov chain. The inference is based on a Bayesian approach involving reversible jump Markov chain Monte Carlo (RJ-MCMC), which allows us to avoid specifying the number of latent regimes in advance. In a simulation study we show how our approach correctly recovers the true configuration of latent regimes with high probability, and that the proposed model can be seen as advantageous with respect to possible competitors. We illustrate through an analysis of two major polluting agents recorded daily at the Danmarksplass site (Norway) in 2022, and their association with certain mixed-frequency weather variables.