Pairwise Likelihood Inference for General State Space Models

This article concerns parameter estimation for general state space models, following a frequentist likelihood-based approach. Since exact methods for computing and maximizing the likelihood function are usually not feasible, approximate solutions, based on Monte Carlo or numerical methods, have to be considered. Here, we concentrate on a different approach based on a simple pseudolikelihood, called “pairwise likelihood.” Its merit is to reduce the computational burden so that it is possible to fit highly structured statistical models, even when the use of standard likelihood methods is not possible. We discuss pairwise likelihood inference for state space models, and we present some touchstone examples concerning autoregressive models with additive observation noise and switching regimes, the local level model and a non-Makovian generalization of the dynamic Tobit model.