Your textbook used a distributed lag model with only current and past values of X_t_-1 coupled with an AR(1)error model to derive a quasi-difference model, where the error term was uncorrelated.
(a)Instead use a static model Y_t = β₀ + β₁X_t + u_t here, where the error term follows an AR(1). Derive the quasi difference form. Explain why in the case of the infeasible GLS estimators you could easily estimate the βs by OLS.
(b)Since φ₁ (the autocorrelation parameter for u_t)is unknown, describe the Cochrane-Orcutt estimation procedure.
(c)Explain how the iterated Cochrane-Orcutt estimator works in this situation. Iterations stop when there is "convergence" in the estimates. What do you think is meant by that?
(d)Your textbook has pointed out that the iterated Cochrane-Orcutt GLS estimator is in fact the nonlinear least squares estimator of the model. Given that -1 < φ₁ < 1, suggest a "grid search" or some strategy to "nail down" the value of $\hat { \phi }$ ₁ which minimizes the sum of squared residuals. This is the so-called Hildreth-Lu method.

Question

Your textbook used a distributed lag model with only current and past values of X_t_-1 coupled with an AR(1)error model to derive a quasi-difference model, where the error term was uncorrelated.
(a)Instead use a static model Y_t = β₀ + β₁X_t + u_t here, where the error term follows an AR(1). Derive the quasi difference form. Explain why in the case of the infeasible GLS estimators you could easily estimate the βs by OLS.
(b)Since φ₁ (the autocorrelation parameter for u_t)is unknown, describe the Cochrane-Orcutt estimation procedure.
(c)Explain how the iterated Cochrane-Orcutt estimator works in this situation. Iterations stop when there is "convergence" in the estimates. What do you think is meant by that?
(d)Your textbook has pointed out that the iterated Cochrane-Orcutt GLS estimator is in fact the nonlinear least squares estimator of the model. Given that -1 < φ₁ < 1, suggest a "grid search" or some strategy to "nail down" the value of

\hat { \phi }

₁ which minimizes the sum of squared residuals. This is the so-called Hildreth-Lu method.

Quizplus · Accepted Answer

The Answer of Your textbook used a distributed lag model with only current and past values of X_t_-1 coupled with an AR(1)error model to derive a quasi-difference model, where the error term was uncorrelated. (a)Instead use a static model Y_t = β₀ + β₁X_t + u_t here, where the error term follows an AR(1). Derive the quasi difference form. Explain why in the case of the infeasible GLS estimators you could easily estimate the βs by OLS. (b)Since φ₁ (the autocorrelation parameter for u_t)is unknown, describe the Cochrane-Orcutt estimation procedure. (c)Explain how the iterated Cochrane-Orcutt estimator works in this situation. Iterations stop when there is "convergence" in the estimates. What do you think is meant by that? (d)Your textbook has pointed out that the iterated Cochrane-Orcutt GLS estimator is in fact the nonlinear least squares estimator of the model. Given that -1 < φ₁ < 1, suggest a "grid search" or some strategy to "nail down" the value of $\hat { \phi }$ ₁ which minimizes the sum of squared residuals. This is the so-called Hildreth-Lu method.

Your Textbook Used a Distributed Lag Model with Only Current ϕ^\hat { \phi }ϕ^​

Your Textbook Used a Distributed Lag Model with Only Current $\hat { \phi }$