Parameter estimation of state space models for univariate observations

Abstract

This paper contributes to the problem of estimation of state space model parameters by proposing estimators for the mean, the autoregressive parameters and the noise variances which, contrarily to maximum likelihood, may be calculated without assuming any specific distribution for the errors. The estimators suggested widen the scope of the application of the generalized method of moments to some heteroscedastic models, as in the case of state-space models with varying coefficients, and give sufficient conditions for their consistency. The paper includes a simulation study comparing the proposed estimators with maximum likelihood estimators. Finally, these methods are applied to the calibration of the meteorological radar and estimation of area rainfall.