Pairwise likelihood inference in state space models with unknown stationary distribution.

We consider stationary state space models for which the stationary distribution is not known analytically. We analyze the problem of static parameter estimation based on pairwise likelihood functions, motivated by the fact that for these general models the evaluation of the full likelihood function is often computationally infeasible. We quantify the bias in stationary models where the invariant distribution is unknown. For these models, an on line Expectation- Maximization algorithm to obtain the maximum pairwise likelihood estimate is developed. We illustrate the method for a linear gaussian model and we give an empirical evidence of our Bias theorem.