Unit root, cointegration and structural changes: Theoretical analyses and improved testing procedures

This dissertation theoretically analyzes various testing procedures for unit root, cointegration and structural change problems and proposes improved procedures.; The first chapter is concerned with unit root tests in the presence of a break in the trend function. In the econometrics literature, unit root procedures designed for an unknown break date assume that a break occurs only under the alternative hypothesis. This is undesirable because the test may reject when the noise is integrated but the trend is changing and the existence of a break is not exploited to improve the power of the test. We propose a procedure that addresses both issues. When a break is present, the limit distribution of the test is the same as in the case of a known break date, which thereby allows increased power while a pre-test and a new trimming device allow controlled size.; The second chapter theoretically compares the asymptotic relative efficiency of the Exp, Mean and Sup type tests for structural change. We show that the Mean type tests are inferior to the Sup and Exp type tests in terms of approximate relative Bahadur efficiency and that the Mean tests are inferior to the Sup tests in terms of the asymptotic relative Pitman efficiency. We also compare tests corrected for potential serial correlation. In this case, the inferiority of the tests based on the Lagrange Multiplier statistics compared to those based on the Wald statistics is pronounced.; The third chapter extends Andrews' (2002) and Andrews and Kim's (2006) end-of-sample instability tests for linear regression models. I propose to apply their procedure after taking quasi-differences of the regression using a consistent estimate of the sum of the coefficients from the autoregressive representation of the error process. The quasi-feasible generalized least squares (QFGLS) version of Andrews and Kim's P test are proposed for cointegration models and the QFGLS version of Andrews' S test for a linear time trend model. The proposed tests are applied to assess the impact Bush's policies have had on the stability of the long-run fiscal stance in the US. The relevant cointegration system breaks down after 2001.