Suppose, we assume that the cointegral relationship may be affected by regime( political or any change). Is there any test or methodology that we can handle this change?
As suggested by Kotosz, you should use unit root tests with structural change (ZA (Zivot and Andrews, 1992) and Perron (1997)). If the variables investigated show the possible existence of trend and structural breaks, in this case, in addition to standard tests, you use the endogenous breakpoint unit root tests of Zivot and Andrews (1992) and Perron (1997).