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

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 functional 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 characteristic function.