Tests for Random Walk Coefficients in State Space Models

This paper deals with testing the constancy of coefficients in regression models against the alternative of following a random walk. Different small sample and asymptotic tests are compared on a Monte Carlo basis. It turns out that the easier to apply large sample tests perform almost as good as the small sample tests. The Locally Best Invariant (LBI) test that is designed only for testing for univariate random walks is extended to multivariate random walks. Here occurs the problem of nuisance parameters that are only present under the alternative. A simple solution is given and Monte Carlo experiments are used to underscore the theoretical results. This paper also extends these tests for random walk coefficients in linear regression models to more general models. More precisely, the assumption that under the null hypothesis all regression coefficients are constant over time is given up. These adapted tests are designed for situations where we already know that some coefficients follow..