Emil Nejstgaard: Theory and Applications in non-linear Cointegrated VAR Models

This PhD dissertation discusses inference and applications in dynamic-mixture cointegrated VAR models, called Autoregressive Conditional Root (ACR) models. These and similar models have found applications to many different data series within macroeconomics and finance. The thesis is comprised of four chapters. Chapter one discusses likelihood-based inference within a general ACR framework where, in particular, we consider consequences for inference when the cointegration relations are considered unknown, we include a restricted constant and let the error covariances be regime dependent. Chapter two discusses an algorithm that allows for estimation of the parameters in the ACR cointegrated model under generalized linear restrictions. In addition, we discuss testing based on likelihood ratio statistics and propose a bootstrap algorithm to simulate their distributions. The properties of the bootstrap is investigated by simulations. Chapter three illustrates the methodology by giving an analysis of two central crude oil prices. In addition, we show that the asymptotic theory of chapter one carries over to a slightly modified version of the model. Finally, chapter four discusses a parameter identification problem that arises in the ACR model as well as in other, similar non-linear autoregressive models.