Structural changes in cointegrated processes

In my dissertation, I show how structural changes in cointegrated processes can be formulated in the vector autoregressive model, how parameters can be estimated, and how one can test for structural changes in the cases where the change points are known or unknown. My dissertation also contains new results about the Granger representation for I(1) processes and a general estimation technique.; Chapter one contains a new proof of the Johansen-Granger representation theorem and derives an explicit expression of the Granger representation. This representation is useful for impulse response analysis and for the asymptotic analysis of cointegrated processes with structural changes.; Chapter two develops the case where potential change points and the number of cointegrating relations are known. The number of cointegrating relations may vary over the sample. I show how a large class of structural changes can be formulated in a unified framework, and that parameters can be estimated with a new estimation technique. This technique is called the generalized reduced rank regression (GRRR) technique, and is described in more detail in Chapter five. Tests for structural changes, and hypotheses that can be expressed by linear parameter restrictions, are shown to have an asymptotic chi 2 distribution. The chapter includes an empirical application to the US term structure of interest rates.; Chapter three considers the case where a change point is unknown. Various tests for parameter constancy are studied. These tests are constructed from a set of likelihood ratio (LR) statistics that test for a structural change in the cointegrating relations over a pre-specified interval. Some tables with critical values are provided along with a study of the power of the different tests.; Chapter four derives a test to determine the number of cointegrating relations in processes with one or multiple structural changes. When the potential change points are known, the asymptotic distribution of the LR test turns out to be a convex combination of squared Dickey-Fuller distributions.; Chapter five presents the most general version of the GRRR technique. Several applications of the estimation technique are presented.