Question 4 (25 marks) a) State whether the following statements are true or false. Briefly justify...

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Question 4 (25 marks) a) State whether the following statements are true or false. Briefly justify your answer. i) In the presence of autocorrelation, the conventionally computed variances and standard errors of forecast values are inefficient. [4 marks] ii) Consistency means that an estimator actually tends toward the parameter, it is supposed to be estimating as power decreases. [4 marks] iii) Autocorrelation biases the coefficients towards zero. [4 marks] b) Table 3 shows the residuals estimated from the following model using 10 observations Y₁ =B₁ + B₂x₂ + B₂x₂ + ex t ê Table 3 5 1 2 3 4 6 7 -0.43 -0.89 1.94 1.22 -0.73 0.34 -1.34 8 9 10 1.05 0.99 0.23 Test for the first-order autocorrelation in the residuals using the Durbin-Watson d statistic at a 1% error level. (hint: Recall the Durbin-Watson d c) Consider the following model: Σ(--1)2 ytan 42 [8 marks] Y₁ Bo+ B₁ X₁ + X2 + µ Suppose the above model error term follows first order autoregressive AR(1). Suggest a remedy to transform this model to be free from autocorrelation problem by assuming p to [5 marks] be known. Question 4 (25 marks) a) State whether the following statements are true or false. Briefly justify your answer. i) In the presence of autocorrelation, the conventionally computed variances and standard errors of forecast values are inefficient. [4 marks] ii) Consistency means that an estimator actually tends toward the parameter, it is supposed to be estimating as power decreases. [4 marks] iii) Autocorrelation biases the coefficients towards zero. [4 marks] b) Table 3 shows the residuals estimated from the following model using 10 observations Y₁ =B₁ + B₂x₂ + B₂x₂ + ex t ê Table 3 5 1 2 3 4 6 7 -0.43 -0.89 1.94 1.22 -0.73 0.34 -1.34 8 9 10 1.05 0.99 0.23 Test for the first-order autocorrelation in the residuals using the Durbin-Watson d statistic at a 1% error level. (hint: Recall the Durbin-Watson d c) Consider the following model: Σ(--1)2 ytan 42 [8 marks] Y₁ Bo+ B₁ X₁ + X2 + µ Suppose the above model error term follows first order autoregressive AR(1). Suggest a remedy to transform this model to be free from autocorrelation problem by assuming p to [5 marks] be known.

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1In cases of high multicollinearity it is possible to assess the individual significance of one or m... View the full answer