I have a question concerning unit-root data and normal distribution. As an assignment, I am checking the long-term relationship between unemployment rates and labor force participation rate. First I used the DF-GLS and KPSS test, and I proved that my data has unit-root at levels and is stationary at first differences. Now I am supposed to use the Johansen cointegration test. As far as I read, it requires normal distribution. Is it possible that my variables with unit-root do not have a normal distribution, and stationary first-differences do? If yes, should I use first differences to Johansen test? 2) I am obligated to run tests on all econometric problems such as autocorrelation, heteroskedasticity etc. should I do it on data with unit root or again stationary first differences?