1．An analyst is estimating whether a fund’s excess return for a month is dependent on interest rates and whether the S& 500 has increased or decreased during the month. The analyst collects 90 monthly return premia (the return on the fund minus the return on the S& 500 benchmark), 90 monthly interest rates, and 90 monthly S& 500 index returns from July 1999 to December 2006. After estimating the regression equation, the analyst finds that the correlation between the regressions residuals from one period and the residuals from the previous period is 0.145. Which of the following is most accurate at a 0.05 level of significance, based solely on the information provided? The analyst:
A) can conclude that the regression exhibits serial correlation, but cannot conclude that the regression exhibits heteroskedasticity.
B) can conclude that the regression exhibits heteroskedasticity, but cannot conclude that the regression exhibits serial correlation.
C) can conclude that the regression exhibits both serial correlation and heteroskedasticity.
D) cannot conclude that the regression exhibits either serial correlation or heteroskedasticity.
The correct answer was D)
The Durbin-Watson statistic tests for serial correlation. For large samples, the Durbin-Watson statistic is equal to two multiplied by the difference between one and the sample correlation between the regressions residuals from one period and the residuals from the previous period, which is 2 × (1 − 0.145) = 1.71, which is higher than the upper Durbin-Watson value (with 2 variables and 90 observations) of 1.70. That means the hypothesis of no serial correlation cannot be rejected. There is no information on whether the regression exhibits heteroskedasticity.
2．An analyst is estimating whether a fund’s excess return for a month is dependent on interest rates and whether the S& 500 has increased or decreased during the month. The analyst collects 90 monthly return premia (the return on the fund minus the return on the S& 500 benchmark), 90 monthly interest rates, and 90 monthly S& 500 index returns from July 1999 to December 2006. After estimating the regression equation, the analyst finds that the correlation between the regressions residuals from one period and the residuals from the previous period is 0.199. Which of the following is most accurate at a 0.05 level of significance, based solely on the information provided? The analyst:
A) can conclude that the regression exhibits multicollinearity, but cannot conclude that the regression exhibits serial correlation.
B) can conclude that the regression exhibits serial correlation, but cannot conclude that the regression exhibits multicollinearity.
C) can conclude that the regression exhibits both serial correlation and multicollinearity.
D) cannot conclude that the regression exhibits either serial correlation or multicollinearity.
The correct answer was B)
The Durbin-Watson statistic tests for serial correlation. For large samples, the Durbin-Watson statistic is approximately equal to two multiplied by the difference between one and the sample correlation between the regressions residuals from one period and the residuals from the previous period, which is 2 × (1 − 0.199) = 1.602, which is less than the lower Durbin-Watson value (with 2 variables and 90 observations) of 1.61. That means the hypothesis of no serial correlation is rejected. There is no information on whether the regression exhibits multicollinearity.
3．Which of the following is least accurate regarding the Durbin-Watson (DW) test statistic?
A) If the residuals have positive serial correlation, the DW statistic will be greater than 2.
B) In tests of serial correlation using the DW statistic, there is a rejection region, a region over which the test can fail to reject the null, and an inconclusive region.
C) If the residuals are uncorrelated, the DW statistic will have a value of 2.
D) If the residuals have negative serial correlation, the DW statistic will be greater than 2.
The correct answer was A)
A value of 2 indicates no correlation, a value greater than 2 indicates negative correlation, and a value less than 2 indicates a positive correlation. There is a range of values in which the DW test is inconclusive.
4．Which of the following is least likely a method of detecting serial correlations?
A) A scatter plot of the residuals over time.
B) The first-order correlation of the residuals over time.
C) The Breusch-Pagan test.
D) The Durbin-Watson test.
The correct answer was C)
The Breusch-Pagan test is a test of the heteroskedasticity and not of serial correlation.
5．An analyst is estimating whether company sales is related to three economic variables. The regression exhibits conditional heteroskedasticity, serial correlation, and multicollinearity. The analyst uses Hansen’s procedure to adjust for the standard errors. Which of the following is most accurate? The:
A) regression will still exhibit heteroskedasticity and multicollinearity, but the serial correlation problem will be solved.
B) regression will still exhibit serial correlation and multicollinearity, but the heteroskedasticity problem will be solved.
C) regression will still exhibit multicollinearity, but the heteroskedasticity and serial correlation problems will be solved.
D) heteroskedasticity, serial correlation, and multicollinearity problems will be solved.
The correct answer was C)
The Hansen procedure simultaneously solves for heteroskedasticity and serial correlation.
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发表于 2008-4-12 16:42
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