Question

12.1. State whether the following statements are true or false. Briefly justify your answer.

a. When autocorrelation is present, OLS estimators are biased as well as inefficient.

b. The Durbin–Watson d test assumes that the variance of the error term ut is homoscedastic.

c. The first-difference transformation to eliminate autocorrelation assumes that the coefficient of autocorrelation rho is -1.

d. The R2 values of two models, one involving regression in the first-difference form and another in the level form, are not directly comparable.

e. A significant Durbin–Watson d does not necessarily mean there is autocorrelation of the first order.

f. In the presence of autocorrelation, the conventionally computed variances and standard errors of forecast values are inefficient.

g. The exclusion of an important variable(s) from a regression model may give a significant d value.

h. In the AR(1) scheme, a test of the hypothesis that rho = 1 can be made by the Berenblutt–Webb g statistic as well as the Durbin–Watson d statistic.

i. In the regression of the first difference of Y on the first differences of X, if there is a constant term and a linear trend term, it means in the original model there is a linear as well as a quadratic trend term.

Answer 1

a. False, because the estimator are unbiased and are not efficient.

b. True, as other assumptions of CLRM are still retained.

c. False, because the assumption is p=+1

d. True, because regressand in the two models must be the same, to compare R² s.

e. True, because it can also signify specification errors.

f. True, as the forecast error involves ², and that is incorrectely estimated by the usual OLS formula.

g. True, because it can also signify specification errors.

h. False, because it can be made only by B-W g statistic, whereas Durbin-Watson table is used to test that p=1.

i. True, write model as then take first diffrence of the given equation. finally verify.