S/F Ekonometri Ch 12.1

Explanation
When autocorrelation is present, OLS (Ordinary Least Squares) estimators are unbiased but inefficient. Autocorrelation refers to the correlation between the error terms in a regression model. In the presence of autocorrelation, the OLS estimators are still unbiased because they still provide the best linear unbiased estimates of the coefficients. However, they become inefficient because the estimated standard errors are no longer valid, leading to less precise estimates. Therefore, the statement that OLS estimators are biased as well as inefficient in the presence of autocorrelation is false.

Explanation
The Durbin-Watson d test assumes that the variance of the error term u is homoscedastic, meaning that the variance of the errors is constant across all levels of the independent variables. This assumption is important because if the errors have different variances, it can affect the accuracy and reliability of the test results. Therefore, it is essential to ensure homoscedasticity before applying the Durbin-Watson d test.

Explanation
The first-difference transformation to eliminate autocorrelation does not assume that the coefficient of autocorrelation (ρ) is -1. This transformation is used to remove the autocorrelation in a time series by taking the difference between consecutive observations. The assumption is that the autocorrelation is not equal to zero, not necessarily -1. Therefore, the correct answer is False.

Explanation
The R^2 values of two models, one involving regression in the first-difference form and another in the level form, are not directly comparable because they represent different concepts. The R^2 value in the first-difference form measures the proportion of the change in the dependent variable that can be explained by the independent variables, while the R^2 value in the level form measures the proportion of the variation in the dependent variable that can be explained by the independent variables. Therefore, comparing these R^2 values directly would not be meaningful.

Explanation
A significant Durbin-Watson d statistic indicates the presence of autocorrelation in the residuals of a regression model. However, it does not necessarily mean that there is autocorrelation of the first order. Autocorrelation of the first order refers to the correlation between consecutive residuals, while the Durbin-Watson test is sensitive to any form of autocorrelation. Therefore, even if there is autocorrelation present in the residuals, it may not be specifically of the first order.

Explanation
Autocorrelation refers to the correlation between a variable and its lagged values. When autocorrelation is present, it means that the current value of a variable is related to its past values. In the context of forecasting, this autocorrelation can lead to inefficiencies in the computation of variances and standard errors of forecast values. This is because the conventional methods assume independence between observations, which is not the case when autocorrelation exists. Therefore, in the presence of autocorrelation, the conventionally computed variances and standard errors of forecast values are inefficient.

Explanation
Excluding an important variable(s) from a regression model can lead to a significant d value because the omission of such variables can result in biased and inaccurate estimates of the relationship between the dependent and independent variables. This can lead to misleading conclusions and incorrect predictions. Therefore, it is important to include all relevant variables in a regression model to ensure accurate and reliable results.

Explanation
The statement is false because the Durbin-Watson d statistic is used to test the hypothesis that ρ = 0, not ρ = 1. The Durbin-Watson test is specifically designed to detect autocorrelation in a time series, while the Berenblutt-Webb g statistic is used for testing the hypothesis that ρ = 1 in an AR(1) scheme. Therefore, the correct answer is false.

Explanation
In the given regression model, if there is a constant term and a linear trend term, it implies that the original model has both a linear and a quadratic trend term. This is because the first difference of Y on the first differences of X captures the change in the variables over time. The constant term represents the intercept, the linear trend term represents the linear change, and if there is also a quadratic trend term, it indicates a curvilinear change in the original model. Therefore, the statement is true.