Time series data often contain only limited information about economic phenomena of interest. In order to learn about these phenomena, one must therefore rely on (at least approximately) efficient inference procedures. In models with nonstandard asymptotic theory, efficient tests must typically be derived from first principles. This is especially difficult in the presence of nuisance parameters under the null hypothesis, yet many models and inference problems fall into this category. This project aims at developing a general set of tools and arguments that allow the construction of asymptotically efficient tests in such an environment. An algorithm is suggested to numerically determine tests in a parametric small sample setting that are almost efficient in the sense that their power comes demonstrably close to an upper bound on the power of all tests. This small sample efficiency is then shown to translate into an asymptotic efficiency property of certain tests. The relevance and feasibility is illustrated by two preliminary applications. The first concerns inference about the value of the cointegrating vector in a bivariate set-up when the common stochastic trend follows a general persistent process, which embeds the usual I(1) assumption as a special case. The second application seeks to develop tests that efficiently discriminate between a single shift form of parameter instability from a random walk-type evolution.
The research project suggests a way forward on a textbook problem in econometric theory, with numerous potential applications. Its contribution is both on a conceptual and computational level, and, in the two worked-out applications, of immediate interest to applied researchers.
Broader Impacts: Although the determination of (almost) efficient tests is numerically involved, this work only needs to be done once for any model and problem. The application to data is entirely straightforward, which should facilitate a widespread adoption by empirical researchers. The project's ideas and results will be disseminated through presentations at universities and conferences, as well as freely available computer code. Finally, through collaborations with graduate students and research assistants, the proposal has a direct impact on student training
