Maximum Likelihood and Prediction Error Methods

Abstract

The basic ideas behind the parameter estimation methods are discussed in a general setting. The application to estimation or parameters in dynamical systems is treated in detail using the prototype problem of estimating parameters in a continuous time system using discrete time measurements. Computational aspects are discussed. Theoretical results in consistency, asymptotic normality and efficiency are covered. Model validation and selection of model structures are discussed. An example is given which illustrates some properties of the methods and shows the usefulness of interactive computing. Additional examples illustrate what happens when the data has different artefacts.