Econometrics question

[Studentka]

Can a time series be stationary in levels and non-stationary in first differences?
On a related note
My dependent variable is I(1), whereas my independent variables are I(0)
If I estimate a regression of the first differences in my dependent variable on all the I(0) variables
Is there a risk of a spurious regression?
Thank you

[lele1987]

according to Granger's theory ,you could not do regression model,I think ,in the situation,you must use the Toda-Yamamoto to solve your problem.