| It is unrealistic to conceive that economic variables or relationships follow a statistical law in which moments or parameters are kept constant over time. The focus of this dissertation is on model specification and testing of time series that are subject to gradual or sudden structural changes in a nonstationary context. Both multivariate and univariate cases are studied. In the former setting, we propose a time varying error correction model in which the cointegrating vector, which may include an intercept, smoothly varies over time. The systemic Johansen's setup is a special case of our model. We model the cointegrating relationship as a dependent and heterogeneously distributed process. A likelihood ratio test on standard (time-invariant) cointegration is defined and its asymptotic distribution is derived. The limiting law is chi-square and it is shown to be a good approximation for finite samples. Moreover, it is shown that the test is asymptotically consistent for a particular class of models. Monte Carlo experiments suggest that the test has power against a general set of time varying alternatives. In an application to the PPP hypothesis with US data, we find strong evidence for time varying parity with Canada, Japan, and several European countries.;Next we propose a model which explains data that is subject to structural changes of unspecified nature in a univariate setting. The structural shifts are generated by a random walk component whose innovations belong to the normal domain of attraction of a symmetric stable law. To test our model against a stationary process, several nonparametric statistics are presented. A Wald test based on spurious regression is also defined. Asymptotic critical values are tabulated because the test distributions are non-standard. Among the procedures considered, we show that the Kwiatkowski et al. (1992), the Breitung (2001), and the Wald test statistics have the best properties in terms of size and power. This approach is applied to a set of international economic variables for which at least one abrupt structural break appears to have occurred. Only for three out of eighteen time series we did not find evidence for sudden structural breaks. |
