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I understand that Dickey-Fuller test could test for a unit root with drift and deterministic time trend. $$ \nabla y_t = a_0+a_1t+\delta y_{t-1}+u_t \ $$

What are the tests for unit root with quadratic trends? In particular, how can I test it in Stata? $$ \nabla y_t = a_0+a_1t+a_2t^2+\delta y_{t-1}+u_t \ $$

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