ARIMA model - unit root test

[ondrejch]

Hello,

I am creating arima model in eviews. My question relates to adf unit root test. I am trying to check whether the original series is stationary or not. When I use adf test with constant or adf test without any exogenous variable, the series is nonstationary and constant is not significant. On the other hand, when I use adf test with trend and constant, the series is stationary. Coefficients in this case are all significant. So, is it possible to say that the series is stationary at level and run arima model with ar(p) and ma(q) using original data? Or do I have to also somehow include the trend in arima model?

I would appreciate any comment.

Thanks