Non-Linear Time Series Modelling with Applications to Equity and Fixed Income Markets

My thesis focuses on theoretical and empirical aspects of modelling time series during different financial and economic conditions. It consists of three separate chapters in which the properties of Threshold Vector Autoregressive Model (TVAR) models are addressed with subsequent applications to equity and fixed income markets. In the first chapter, which is a joint work with my supervisor Lars Stentoft, we examine the steady state properties of the TVAR model. Assuming the trigger variable is exogenous and the regime process follows a Bernoulli distribution, we derive the necessary and sufficient conditions for existence of a stationary distribution. The derived stationarity conditions for the TVAR model could help to validate existing and future empirical studies, which are using this type of framework. We analyze a situation related to so called locally explosive models, where the stationary distribution exists though the model is explosive in one regime. Using simulation methods we show that locally explosive models can generate some of the key properties of financial and economic data, usually implied by the literature on bubble formation. Thus, having closed form solutions for the stability properties, which describe locally explosive models, could be potentially useful for the studies of bubbles in a multivariate setting. We also demonstrate that assessing the stationarity of threshold models based on simulations might well lead to wrong conclusions, which highlights the challenges when making inference in non-linear threshold models