# Nonlinear methods for detecting and measuring the strength of a trend in the context of unit roots

I am looking for statistical methods to detect the presence and strength of a trend in the context of unit root testing.

We could for instance use a trend-stationarity ADF test:

Here the t-statistic of the $\delta$ coefficient could help us determine the strength of a linear trend.

However, the test will fail in the case of another functional form of the trend, for instance when the trend is quadratic.

Are there therefore more generic methods, that can cope with testing for such alternative trends (linear, quadratic, other)?

• Are you interested in trends specifically in the context of unit root testing? – Richard Hardy Sep 19 '17 at 8:11
• Preferably yes as they seem to me more persistent. – JohnAndrews Sep 19 '17 at 8:13
• Perhaps you should edit the title and the body to make this clearer (thanks for having edited the tags already). – Richard Hardy Sep 19 '17 at 8:16