Question

In estimating a regression based on monthly observations from January 1987 to December 2002 inclusive, you find that the coefficient on the independent variable is positive and significant at the 0.05 level. You are concerned, however, that the t−statistic on the independent variable may be inflated because of serial correlation between the error terms. Therefore, you examine the Durbin-Watson statistic, which is 1.8953 for this regression. (3.1) Based on the value of the Durbin-Watson statistic, what can you say about the serial correlation (3) between the regression residuals? Are they positively correlated, negatively correlated, or not correlated at all? In estimating a regression based on monthly observations from January 1987 to December 2002 inclusive, you find that the coefficient on the independent variable is positive and significant at the 0.05 level. You are concerned, however, that the t−statistic on the independent variable may be inflated because of serial correlation between the error terms. Therefore, you examine the Durbin-Watson statistic, which is 1.8953 for this regression.

(3.1) Based on the value of the Durbin-Watson statistic, what can you say about the serial correlation between the regression residuals? Are they positively correlated, negatively correlated, or not correlated at all? (3 marks)

Answer 1

Durbin watson statistic tells us about the autocorrelation in residuals. Normally, the statistic is between 1.5 to 2.5. If the value falls outside this range, it is a cause of concern.

If the statistic is equal to 2, there is no autocorrelation at all. If the value is between 0-2, there is a positive correlation. If the value is between 2-4, there is a negative correlation.

As the Durban watson statistic is 1.8953 in this case, there is a positive correlation between the residuals. It is common in time series data and it is not a cause of concern as it lies between 1.5 and 2.5.