Authors

• Juan Carlos Escanciano (jescanci@unav.es)
  School of Economics and Business Administration, University of Navarra

Abstract
Economic theories in dynamic contexts usually impose certain restrictions on the conditional mean of the underlying economic variables. Omnibus specification tests are the primary tools to test such restrictions when there is no information on the possible alternative. In this paper we study in detail the power properties of a large class of omnibus specification tests for parametric conditional means under time series processes. We show that all omnibus specification tests have a preference for a finite-dimensional space of alternatives (usually unknown to the practitioner) and we characterize such space for Cram'r-von Mises (CvM) tests. This fact motivates the use of optimal tests against such preferred spaces instead of the omnibus tests. We proposed new asymptotically optimal directional and smooth tests that are optimally designed for cases in which a finite-dimensional space of alternatives is in mind. The new proposed optimal procedures are asymptotically distribution-free and are valid under weak assumptions on the underlying data generating process. In particular, they are valid under possibly time varying higher conditional moments of unknown form, e.g., conditional heteroskedasticity. A Monte Carlo experiment shows that previous asymptotic results provide good approximations in small sample sizes. Finally, an application of our theory to test the martingale difference hypothesis of some exchange rates provides new information on the rejection of omnibus tests and illustrates the relevance of our results for practitioners.

Classification JEL:C12; C14; C52

Number of Pages:42

Creation Date:2005-05-01

Number:null/05