Alternative Asymptotically Optimal Tests and Their Application to Dynamic Specification

Abstract

A method is presented for generating test statistics which share the same first order asymptotic optimality properties of the classical statistics. Generalizing Neyman's (1959) work, the linearised classical statistic tests restrictions in implicit function form using a parameter estimator which is consistent and asymptotically normally distributed under the alternative hypothesis. By judicious choice of estimator and form of restrictions at which to evaluate the statistic, a class of asymptotically optimal statistics is obtained among which are numbered some familiar classical statistics. An application is presented for testing common factor restrictions in a single equation dynamic regression model with moving average disturbances.