# More than one unit root

I'm wondering how to detect the existence of more than one unit root. I've tested the non-stationnarity of my serie using the strategy of test of Dickey-Fuller (joint hypothesis: Fisher), and I detect unit root. however, after differencing the serie, I think that it's still non stationary and it has another unit root. My questions are:

1. How can I detect more than one unit root

2. Am i obliged to apply the strategy of Fisher of Dickey-fuller again to the differienced serie or since I did not detect a trend in the level serie I'll not detect it in the differencing one?

• Point 2. is correct: you apply ADF test repeatedly but you normally discard the possibility for trend or constant for higher-order unit roots (no trend for root number two, no trend or intercept for higher order roots). – Richard Hardy Apr 7 '16 at 13:19
• So if I understand well, i apply the test of DF to the differiencied serie to detect the second unit root ? – user109464 Apr 7 '16 at 13:55
• Yes, you do that. – Richard Hardy Apr 7 '16 at 13:55