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Unformatted text preview: DGP: Y = X 1 & 1 + X 2 & 2 + e; e s N (0 T & 1 ; ± 2 I T ) Reg. equation: Y = X 1 & 1 + e; e s N (0 T & 1 ; ± 2 I T ) Is ^ & 1 unbiased? Prove your answer. Problem 5 SangHee wants to forecast the dependent variable at time T + 1 , y T +1 by estimating the following regression equation Y = X& + e; e s N (0 T & 1 ; ± 2 I T ) (1) What is the forecasts of y T +1 ? (2) What is the nature of prediction error? Explain your answer by deriving the variance of prediction error. 1 Problem 6 Brie&y explain the following notions: (1) Unit root process (2) Unit root test (3) Cointegration (4) Stationary process (5) Spurious regression Problem 7 Consider the following model y i = & + e i , e i s i : i : d :N (0 ; 1) (1) Construct the log likelihood function. (2) Derive the maximum likelihood estimator of & . (3) Derive Var( ^ & ). 2...
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 Spring '09
 gtewewa
 Normal Distribution, Maximum likelihood, Estimation theory, Likelihood function, Bias of an estimator

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