Asymptotic quasi-likelihood based on kernel smoothing for nonlinear and non-gaussian state-space models

This paper considers parameter estimation for nonlinear and non-Gaussian state-space models with correlation. We propose an asymptotic quasi-likelihood (AQL) approach which utilises a nonparametric kernel estimator of the conditional variance covariances matrix Σt to replace the true Σt in the standard quasi-likelihood. The kernel estimation avoids the risk of potential miss-specification of Σt and thus make the parameter estimator more robust. This has been further verified by empirical studies carried out in this paper.