Quasi-likelihood ratio tests for cointegration, cobreaking, and cotrending
针对同时存在随机趋势和断点线性趋势的变量，提出了三种拟似然比检验，分别用于判断协整、协整与协突变同时成立、以及协整与协趋势同时成立。
We consider a set of variables with two types of nonstationary features, stochastic trends and broken linear trends. We develop tests that can determine whether there is a linear combination of these variables under which the nonstationary features can be canceled out. The first test can determine whether stochastic trends can be eliminated and thus whether cointegration holds, regardless of whether structural breaks in linear trends are eliminated. The second test can determine whether both stochastic trends and breaks in linear trends are simultaneously removed and thus whether cointegration and cobreaking simultaneously hold. The third test can determine whether not only breaks in linear trends but also linear trends themselves are eliminated along with stochastic trends and thus whether both cointegration and cotrending hold.