Testing Stationarity for Unobserved Components Models

Unobserved components (UC) models are widely used to estimate stochastic trends in macroeconomic time series, with the existence of a stochastic trend typically motivated by a stationarity test. However, given the small sample sizes available for most macroeconomic variables, standard Lagrange multiplier tests of stationarity will perform poorly when the data are highly persistent. To address this problem, we propose the alternative use of a likelihood ratio test of stationarity based on a UC model and demonstrate that a bootstrap version of this test has far better small-sample properties for empirically-relevant data generating processes than bootstrap versions of the standard tests. An application to U.S. real GDP produces stronger support for the presence of large permanent shocks when using the likelihood ratio test as compared to standard tests.