Asymptotic Theory of a Test for the Constancy of Regression Coefficients Against the Random Walk Alternative

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. The LBI (locally best invariant) test is suggested under normality for the constancy of regression coefficients against the altemative hypothesis that one component of the coefficients follows a random walk process. We discuss the limiting null behavior of the test statistic without assuming normality under two situations, where the initial value of the random walk process is known or unknown. The limiting distribution is that of a quadratic func-tional of Brownian motion and the characteristic function is obtained from the Fredhohm determinant associated with a certain integral equation. The limiting distribution is then computed by numerical inversion of the char-acteristic function.