Three Essays on Unit Roots and Nonlinear Co-Integrated Processes

Abstract

<p>Many macroeconomic and financial key variables such as e.g. consumption, investment, gross domestic product and interest rates, display non-stationary features such as trends or changing variances. A non-stationary stochastic process that can be made stationary by taking first differences, is called ingrated of order one. If several variables are integrated of order one, then there may exist a linear combination of the variables such that the resulting process is stationary. Integrated processes with this property are said to be cointegrated. The concept of cointegration, introduced by Granger (1981) and Engle and Granger (1987), allows to describe equilibrium relationships between economic variables and, hence, bridges the gap between time series analysis and economics. For this reason, cointegration has become a popular tool for applied econometric work, e.g. Johansen and Juselius (1992).<br /> In the last 25 years, both integrated and cointegrated processes have attracted a lot of attention in theoretical and applied time series econometrics. The seminal contributions by Dickey and Fuller (1979), Engle and Granger (1987), Phillips and Perron (1988) and Johansen (1988, 1991) have provided a solid basis for numerous extensions of this field of research.<br /> This dissertation sheds light on two important extensions of the unit root model and the linear vector error correction model (VECM). In the first chapter, I extend several state-of-the-art unit root tests in the presence of permanent variance changes and compare their finite sample behavior in an extensive simulation study. In the two remaining chapters, I concentrate on error correction models that allow for a nonlinear adjustment process. The second chapter is devoted to the statistical inference of a general three regime threshold VECM. In chapter three, I explore the dynamics of spot and future prices using a novel nonlinear error correction model.</p>