Exact score and information matrix for panel hidden semi-Markov models

We describe a general multivariate hidden semi-Markov model for time series and panel data. The model entails multiple response variables arising from exponential families conditionally on covariates and a discrete time-varying latent variable. The latter is modeled through transition probabilities and sojourn time distributions. We derive efficient forward recursions to exactly compute the score and information matrix. In a simulation study we show the validity of our inferential approach for parameter and standard error estimation. The approach is also illustrated on an original real data example on sales of four arm types from member countries of the North Atlantic Treaty Organization to non-member countries in the period 2002-2022.