A composite likelihood consists in a combination of valid likelihood objects, usually related to small subsets of data. The merit of composite likelihood is to reduce the computational complexity so that it is possible to deal with large datasets and very complex models, even when the use of standard likelihood or Bayesian methods is not feasible. In this paper, we aim to suggest an integrated, general approach to inference and model selection using composite likelihood methods. In particular, we introduce an information criterion for model selection based on composite likelihood. Applications to modelling time series of counts through dynamic generalized linear models and to the analysis of the well-known Old Faithful geyser dataset are also given.

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

This paper reviews some recent results on the construction of improved prediction limits for time series models and presents a simple solution based on a fully conditional approach. A prediction limit, expressed as a modification of the estimative one, is obtained so that its conditional and unconditional coverage probability equals the target value to third-order accuracy. Although the specification of the ancillary statistic is not required, it respects the conditionality principle, to the relevant order of approximation. Moreover, the corresponding predictive density is specified in a relatively simple closed form. Simple examples show the usefulness of this conditional approach to prediction.

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