## Abstract

We consider variables with two types of non-stationary features, that is, stochastic and broken linear trends, and develop tests that can be used to see if there exists a linear combination of given variables under which these non-stationary features can be canceled out. In particular, the first test we develop can be used to see if stochastic trends can be eliminated and thus cointegration holds, regardless of whether or not breaks in linear trends are eliminated. The second test is to see if both stochastic trends and breaks in linear trends are simultaneously removed and thus both cointegration and cobreaking simultaneously hold. The third test is to see if not only breaks in linear trends but also linear trends themselves are eliminated along with stochastic trends and thus both cointegration and cotrending hold. We provide the asymptotic null distributions of proposed test statistics and some Monte Carlo simulations results to assess the adequateness of our asymptotic distributions in samples with common sizes.