A Randomised Test to Distinguish Time‐Varying Coefficient Models

ABSTRACT Time‐varying coefficient models have drawn great attention in both theoretical and empirical research. This article introduces two consistent tests, based on a randomised procedure, to distinguish whether time‐varying coefficients behave as deterministic functions of time or as unit root processes. By formulating the null hypothesis for each specification, we establish that the proposed test statistics asymptotically follow a chi‐squared distribution under their respective null hypotheses and diverge to infinity in probability under their respective alternative hypotheses. Simulation studies demonstrate the satisfactory performance of both test statistics in finite samples. Furthermore, we apply the proposed tests to analyse various financial and macroeconomic datasets. The results of the tests reveal that deterministic functions of time should be adopted for these applications.