The estimation of a state space model by estimating functions with an application

Conventionally the parameters of a linear state space model are estimated by maximizing a Gaussian likelihood function, even when the input errors are not Gaussian. In this paper we propose estimation by estimating functions fulfilling Godambe's optimality criterion. We discuss the issue of an unknown starting state vector, and we also develop recursive relations for the third- and fourth-order moments of the state predictors required for the calculations. We conclude with a simulation study demonstrating the proposed procedure on the estimation of the stochastic volatility model. The results suggest that the new estimators outperform the Gaussian likelihood.