An Exact Test for a Stochastic Coefficient in a Time Series Regression Model

An exact small‐sample test is developed for testing the hypothesis that a regression coefficient is constant against the alternative that it is generated by a random walk process. The test is mean‐ and scale‐invariant and approximates the most powerful invariant test against any specific alternative. It thus outperforms tests previously given in the literature. Computationally efficient algorithms are given to compute the test statistic and its distribution using a modified version of the Kalman filter.