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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:
Yi = β0 + β1Xi + ui
ui = ρui-1 + vi; < 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(= Xj)and j-1, how would you proceed? Would you use the information on the lagged residual at all? Why or why not?
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