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Assume That You Had Found Correlation of the Residuals Across

question 17

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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+uiui=ρui1+vi;ρ<1.\begin{array} { c } Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i } \\u _ { i } = \rho u _ { i - 1 } + v _ { i } ; | \rho | < 1 .\end{array}
Furthermore, assume that you had obtained consistent estimates for β0,β1,ρ\beta _ { 0 } , \beta _ { 1 } , \rho . If asked to make a prediction for YY , given a value of X(=Xj)X \left( = X _ { j } \right) and u^j1\hat { u } _ { 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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