Composite Likelihood Function in State Space Models.

In general state space models, where the computational effort required in the evaluation of the full likelihood function is infeasible, we analyze the problem of static parameter estimation based on composite likelihood functions, in particular pairwise likelihood functions. We discuss consistency and efficiency properties of the estimators obtained by maximizing these functions in state space scenario, linking these properties to the characteristics of the model. We empirically compare the efficiency between maximum pairwise likelihood and maximum full likelihood estimators. We suggest the existence of a ‘best’ distance between pairs of observations, in terms of variance of the maximum pairwise likelihood estimator.