Powerful Autocorrelation Robust Testing in Finite Samples

In many disciplines data are recorded over time. Such data are then often analyzed with regression models, and decisions are based on the outcome of tests of statistical hypotheses concerning a linear restriction on the regression coefficients. Since the data are recorded over time, they are frequently strongly autocorrelated. Therefore it is inevitable that the tests used are ``autocorrelation robust in the sense that they are not ``distorted by the presence of autocorrelation in the data. Unfortunately, in Preinerstorfer and Pötscher (2013) and Preinerstorfer (2014) we have shown analytically that standard procedures used in practice will lead to wrong decisions with high probability if the autocorrelation in the data is strong, i.e., the standard procedures available are not autocorrelation robust. We have also shown (under certain technical assumptions) how existing tests can be adjusted to obtain autocorrelation robust tests. Our adjustments are based on additional invariance properties that amount to effectively ignoring a certain part of information in the data from the outset. Even though our adjustments often yield valid tests, there remain many challenging open questions concerning: (1) the improvement of these adjusted tests by using the data to decide if (and which) information in the data should be ``ignored; (2) the applicability of the adjustment procedures to other testing problems than linear equality restrictions (e.g., testing one-sided hypotheses or testing for structural breaks in the regression coefficients at an unknown time point); and (3) the generalizability of this approach to other models (e.g., dynamic, non-linear, or non-parametric models). The goal of the proposed project is to optimize the adjusted tests with respect to their power properties, and then to extend these powerful procedures to more general hypothesis testing problems and to a large variety of models.