Assume That You Had Found Correlation of the Residuals Across $| \rho |$

question 17

Essay

Assume that you had found correlation of the residuals across observations. This may happen because the regressor is ordered by size. Your regression model could therefore be specified as follows:
Y_i = β₀ + β₁X_i + u_i
u_i = ρu_i-1 + v_i; $| \rho |$ < 1.
Furthermore, assume that you had obtained consistent estimates for β₀, β₁, ρ. If asked to make a prediction for Y, given a value of X(= X_j)and $\hat u$ _j-1, how would you proceed? Would you use the information on the lagged residual at all? Why or why not?