# Help Finding Information on “Power Trends” or “Polynomial Trends”

I need to prove some facts about the asymptotic OLS estimator, $\hat{\delta}$ in model: $y_t = \alpha_t + \delta \cdot t^b + \epsilon_t$ where $\epsilon_t \sim iid(0,\sigma^2)$.

I've looked at the example where $b=1$ in Hamilton, and have tried to generalize the $Y_t$ matrix he uses:

[$T^{-1/2}$,0;0,$T^{-3/2}$]

to

[$T^{-1/2}$,0;0,$T^{-(b+2)/2}$]

but am not getting convergence.

• Is $\alpha$ time-variant? (Because it has a t-subscript) – Alecos Papadopoulos Apr 10 '16 at 22:35