Abstract
Average exponential F tests for structural change in a Gaussian linear regression model and modifications thereof maximize a weighted average power that incorporates specific weighting functions to make the resulting test statistics simple. Generalizations of these tests involve the numerical evaluation of (potentially) complicated integrals. In this paper, we suggest a uniform Laplace approximation to evaluate weighted average power test statistics for which a simple closed form does not exist. We also show that a modification of the avg-F test is optimal under a very large class of weighting functions and can be written as a ratio of quadratic forms so that both its p-values and critical values are easy to calculate using numerical algorithms.
Highlights
Andrews, Lee and Ploberger (1996) suggest finite sample similar tests for structural change at unknown change-points in the Gaussian linear regression model which maximize a weighted average power (WAP)
Existing WAP tests for structural change at unknown changepoints have three drawbacks. (i) First, they need to incorporate specific weighting functions to make the functional forms of the resulting test statistics simple
The use of different weighting functions to accommodate the relative importance of different departures from the null hypothesis would not be viable because of the need to evaluate complicated integrals numerically. (ii) Second, it is difficult to make a case for any particular weighting function, and one may argue that the optimality of a particular test depending on a specific weighting function may be of little value for different researchers. (iii) Third, existing WAP tests require the evaluation of several F-tests for all possible change-points
Summary
Andrews, Lee and Ploberger (1996) suggest finite sample similar tests for structural change at unknown change-points in the Gaussian linear regression model which maximize a weighted average power (WAP). They obtain a class of optimal tests for the case where the disturbance variance is known. For the case where the error variance is unknown, they propose replacing the unknown variance by an estimate and show that the resulting tests are still similar and asymptotically optimal (see Andrews and Ploberger (1994)). For the case where the error variance is unknown, they propose replacing the unknown variance by an estimate and show that the resulting tests are still similar and asymptotically optimal (see Andrews and Ploberger (1994)). Forchini (2002) extends the results of Andrews, Lee and Ploberger (1996), and derives similar WAP tests for structural change at unknown change-points in the Gaussian linear regression model that allow for an unknown
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