I am using panel data for my analysis.My dependent variable is non-stationary while all my explanatory variables are stationary.Also my dependent variable is a bounded variable( an index variable having range between 0 and 1, which has been constructed by me).I am not sure of whether I can take the log of a bounded variable(to make it stationary)? Please give me some suggestion as to how i should deal with this non stationarity problem in dependent variable?