Exact distribution theory for the maximum likelihood estimators of local trend models

This thesis has two distinct parts. The second and third chapters concern the theory and practical implementation of computing the value of the (possibly multivariate) distribution function from the known characteristic function. The remaining four chapters consist of a study of the distributional behaviour of the maximum likelihood estimator of some local trend models. The motivation of the work is the paucity of our knowledge of the behaviour of the maximum likelihood estimator of local trend models. These types of models are being increasingly used in the social sciences, but little is actually known about their theoretical behaviour, especially when we have only small sample sizes.