what is the stats for long run cointegration how to test cointegration whose data do i need for er test is the first difference a cointegration variable? what are the long run cointegration tests how to use unit roots test long run cointegration test why does ardl test for cointegration why are unit root statistics not valid which unit test is used to test for first differences? does the long run cointegration test when does er test for cointegration of first data? how do long run cointegration tests work why is the err test valid does ardl test cointegration when to test cointegration for long run which long run cointegration statistic for first differences what tests can be used for first differences what tests can be run for first differences which variable is not considered long run cointegration