1st difference vs. 2nd difference

[d_c]

Hi,

I'm working on a forecasting a data set. I took the log of the data and conducted an unit root test. The test results were failed to reject so I proceed w/taking the 1st difference of the data. The 1st difference of the graph seemed a lot better but I do not know if this is looks "covariance stationary" enough. There's less volatility in the graph but my concern is that the data doesn't look too constant and it doesn't really centered around 0...I took the 2nd difference and the mean and variance look really constant and are centered around 0. Does the 1st difference look okay? I'm not sure if I'll be okay if I proceed with the 1st difference. My model has to be covariance stationary before I can use any ARMA terms. Please help!

http://imageshack.us/f/59/1stvs2nddifference.jpg/