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During the course of a multiple regression analysis, an analyst has observed several items that she believes may render incorrect conclusions. For example, the coefficient standard errors are too small, although the estimated coefficients are accurate. She believes that these small standard error terms will result in the computed t-statistics being too big, resulting in too many Type I errors. The analyst has most likely observed which of the following assumption violations in her regression analysis?

Positive serial correlation is the condition where a positive regression error in one time period increases the likelihood of having a positive regression error in the next time period. The residual terms are correlated with one another, leading to coefficient error terms that are too small.

Alex Wade, CFA, is analyzing the result of a regression analysis comparing the performance of gold stocks versus a broad equity market index. Wade believes that serial correlation may be present, and in order to prove his theory, should use which of the following methods to detect its presence?

A)	The Breusch-Pagan test.

B)	The Durbin-Watson statistic.

C)	The Hansen method.

A)	The Breusch-Pagan test.

B)	The Durbin-Watson statistic.

C)	The Hansen method.

The Durbin-Watson statistic is the most commonly used method for the detection of serial correlation, although residual plots can also be utilized. For a large sample size, DW ≈ 2(1-r), where r is the correlation coefficient between residuals from one period and those from a previous period. The DW statistic is then compared to a table of DW statistics that gives upper and lower critical values for various sample sizes, levels of significance and numbers of degrees of freedom to detect the presence or absence of serial correlation.

Which of the following statements regarding serial correlation that might be encountered in regression analysis is least accurate?

A)	Negative serial correlation causes a failure to reject the null hypothesis when it is actually false.

B)	Positive serial correlation typically has the same effect as heteroskedasticity.

C)	Serial correlation occurs least often with time series data.

Which of the following statements regarding serial correlation that might be encountered in regression analysis is least accurate?

A)	Negative serial correlation causes a failure to reject the null hypothesis when it is actually false.

B)	Positive serial correlation typically has the same effect as heteroskedasticity.

C)	Serial correlation occurs least often with time series data.

Serial correlation, which is sometimes referred to as autocorrelation, occurs when the residual terms are correlated with one another, and is most frequently encountered with time series data.

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 multicollinearity, but the heteroskedasticity and serial correlation problems will be solved.

C)	regression will still exhibit serial correlation and multicollinearity, but the heteroskedasticity problem will be solved.

A)	regression will still exhibit heteroskedasticity and multicollinearity, but the serial correlation problem will be solved.

B)	regression will still exhibit multicollinearity, but the heteroskedasticity and serial correlation problems will be solved.

C)	regression will still exhibit serial correlation and multicollinearity, but the heteroskedasticity problem will be solved.

The Hansen procedure simultaneously solves for heteroskedasticity and serial correlation.

Which of the following is least likely a method of detecting serial correlations?

A)	The Durbin-Watson test.

B)	The Breusch-Pagan test.

C)	A scatter plot of the residuals over time.

Which of the following is least likely a method of detecting serial correlations?

A)	The Durbin-Watson test.

B)	The Breusch-Pagan test.

C)	A scatter plot of the residuals over time.

The Breusch-Pagan test is a test of the heteroskedasticity and not of serial correlation.

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)	If the residuals have negative serial correlation, the DW statistic will be greater than 2.

C)	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.

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)	If the residuals have negative serial correlation, the DW statistic will be greater than 2.

C)	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.

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.

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 serial correlation, but cannot conclude that the regression exhibits multicollinearity.

B)	cannot conclude that the regression exhibits either serial correlation or multicollinearity.

C)	can conclude that the regression exhibits multicollinearity, but cannot conclude that the regression exhibits serial correlation.

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&

A)	can conclude that the regression exhibits serial correlation, but cannot conclude that the regression exhibits multicollinearity.

B)	cannot conclude that the regression exhibits either serial correlation or multicollinearity.

C)	can conclude that the regression exhibits multicollinearity, but cannot conclude that the regression exhibits serial correlation.

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.

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)	cannot conclude that the regression exhibits either serial correlation or heteroskedasticity.

B)	can conclude that the regression exhibits serial correlation, but cannot conclude that the regression exhibits heteroskedasticity.

C)	can conclude that the regression exhibits heteroskedasticity, but cannot conclude that the regression exhibits serial correlation.

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)	cannot conclude that the regression exhibits either serial correlation or heteroskedasticity.

B)	can conclude that the regression exhibits serial correlation, but cannot conclude that the regression exhibits heteroskedasticity.

C)	can conclude that the regression exhibits heteroskedasticity, but cannot conclude that the regression exhibits serial correlation.

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.