Consider the following simple regression model with an AR(1) error. Assume that E(e) = 0, var(e)...

 

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Consider the following simple regression model with an AR(1) error. Assume that E(e) = 0, var(e) = 21, cov(e₁, u₁-m) = 0 and cov(e₁, X₁p) = 0, for all i (i = 1, 2, n), for all m (m = 1, 2,..., i), and for all p (p = 0, 1, 2,..., i). (a) (b) y₁ = BX, +u; u; = pu₁_₁ +e; Let us assume that p<1, 00 #0 and 0p=0 for p≥1. Explain why you cannot estimate ß by OLS (ordinary least squares) in this case, and also explain how you will estimate B. [10] Now assume that p=1 and 0₁=0 for p20. Assuming u₁ = 0, find the variance- covariance matrix of u, var(u). Explain if you can estimate ß by GLS (generalized least squares). [10] Consider the following simple regression model with an AR(1) error. Assume that E(e) = 0, var(e) = 21, cov(e₁, u₁-m) = 0 and cov(e₁, X₁p) = 0, for all i (i = 1, 2, n), for all m (m = 1, 2,..., i), and for all p (p = 0, 1, 2,..., i). (a) (b) y₁ = BX, +u; u; = pu₁_₁ +e; Let us assume that p<1, 00 #0 and 0p=0 for p≥1. Explain why you cannot estimate ß by OLS (ordinary least squares) in this case, and also explain how you will estimate B. [10] Now assume that p=1 and 0₁=0 for p20. Assuming u₁ = 0, find the variance- covariance matrix of u, var(u). Explain if you can estimate ß by GLS (generalized least squares). [10]

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Estimating in a Simple Regression with AR1 Errors Youve presented two scenarios for a simple regression model with an AR1 error term a p 1 and 0 In th... View the full answer