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)?