Revision with unchanged content. 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 book is on model specification and testing of time series that are subject to gradual or sudden structural changes in a nonstationary context. In the multivariate setting, we propose a time varying error cor-rection model in which the cointegrating vector smoothly varies over time. The systemic Johansen's setup is a special case of our model. A likelihood ratio test on standard cointegration is defined and its asymptotic distribution is derived. In an application to the PPP hypothesis with US data, we find strong evidence for parity with several world 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. This approach is applied to a set of international economic variables for which at least one abrupt structural break appears to have occurred. The book is addressed to researchers and graduate students in economics whose main interest is in theoretical and applied cointegrated.