What is meant by linear time series model with IID errors?

Question

I was asked to estimate a linear time series model with IID errors. I am not sure what this means and the professor is not getting back to me. Does this mean to just estimate a pooled OLS on the time series data?

Answer 1

Linearity in this context usually means that the partial derivative of the model's expected value is independent of the coefficients, i.e., $$ X_t = \phi_1 X_{t-1} + \phi_2 X_{t-2} + \epsilon_t, $$
thus $$ \frac{\partial}{\partial \phi_1} E[X_t| X_{t-1} = x_{t-1}, X_{t-2} = x_{t-2}] = x_{t-1}. $$

Indeed you can estimate the coefficients using OLS.