  Latent autoregressive models are useful time series models for the analysis
of infectious disease data. Evaluation of the likelihood function of latent
autoregressive models is intractable and its approximation through
simulation-based methods appears as a standard practice. Although simulation
methods may make the inferential problem feasible, they are often
computationally intensive and the quality of the numerical approximation may be
difficult to assess. We consider instead a weighted pairwise likelihood
approach and explore several computational and methodological aspects including
estimation of robust standard errors and the role of numerical integration. The
suggested approach is illustrated using monthly data on invasive meningococcal
disease infection in Greece and Italy.
