This paper discusses computationally efficient methods for exact maximum-likelihood estimation of parameters in state-space models. The proposed strategy is based on direct maximisation of the likelihood function, and it can be applied to a wide range of practical univariate and multivariate models. Almost no extra computing is required to deal with diffuse initial conditions. Practical problems, such as missing values and non-equal spacing, are dealt with in a straightforward fashion. Applications are given for structural time-series models, nonparametric splines, and models for heteroskedasticity.
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