A Spatio-Temporal Hidden Markov Model with an Application to Italian Unemployment Data

We introduce a spatio-temporal hidden Markov model with covariates, which includes distinct spatial and temporal components governing the latent process. In the proposed model, the vector of regression coefficients, including the intercept, can be assumed to be partially or completely dependent on the latent state. The proposed model is estimated within a Bayesian framework by an approximate exchange algorithm. We evaluate the proposed approach using both synthetic and real datasets. In particular, for the empirical application, we investigate regional unemployment rates in Italy, incorporating socio-economic indicators alongside linear and quadratic temporal trends to capture regional and temporal heterogeneity.