Testing for Random Walk Coefficients in the Presence of Varying Coefficients Under H₀

Abstract

This chapter is devoted to testing for random walk coefficients in state space models, where some coefficients are already known to vary over time. The tests proposed so far are not suitable for this situation since now even under the null hypothesis some coefficients are time varying. However, after a simple transformation of the regression equation these tests may be applied again. Thereby one is enabled to test also which coefficients vary over time. Unfortunately, the asymptotic distribution can only be derived when all regressors are stationary variables, simulations show however that the methods proposed here also work when I(1) regressors are present.