The analysis of the inherent structure of time-dependent data is crucial for the selection of a suitable model. This thesis is comprised of three self-contained essays on time series models and the identification of their stability properties. Hypothesis tests are particularly useful in this context. While the first chapter presents a unit root test that is robust against an unknown nonparametric trend, the second chapter deals with testing for structural change in linear regression models. The third chapter is devoted to the analysis of the functional dependence structure of bond yields with different maturities, and discusses the identification and estimation of a functional factor model for yield curves from the perspective of functional data analysis
