n analyst is estimating whether a fund’s excess return for a month is dependent on interest rates and whether the S&P 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&P 500 benchmark), 90 monthly interest rates, and 90 monthly S&P 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) cannot conclude that the regression exhibits either serial correlation or heteroskedasticity. Your answer: B was incorrect. The correct answer was C) cannot conclude that the regression exhibits either serial correlation or heteroskedasticity. 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. --------- if we fail to reject the null (H0: serial correlation = 0), doesnt that imply we have serial correlation and the answer should be A?
It is my understanding that in all of these test (for conditional heteroskedasticity, serial correlation, etc.) the H0 assumption is that serial correlation (or conditional heteroskedasticity IS NOT present So if you cannot reject the null, that means that there is no serial correlation Please correct me if I’m wrong, this is definitely my weak topic…
that’s what i said.
pacmandefense Wrote: ------------------------------------------------------- > if we fail to reject the null (H0: serial > correlation = 0), doesnt that imply we have serial > correlation and the answer should be A? if you fail to reject the hypothesis “no serial correlation” then it would suggest there’s no serial correlation
If we fail to reject the null, we cannot reject the null, the null is correct, serial correlation=0??? Or am I going crazy?
i think you’re correct knut, it’s just the double negatives obfuscating the answer
nevermind, i drew out the line graph thingy and it figured it out. i need to sleep.
This is correct… ya_ne_knut Wrote: ------------------------------------------------------- > If we fail to reject the null, we cannot reject > the null, the null is correct, serial > correlation=0??? > > Or am I going crazy? Trap: Some times CFAI says in the question that the auto-correlation of residuals was found based on some AR modeled equation. If that is the case, the D-W test doesnt work. The T-stat would be = Estimated Auto Correlation/Standard Error(Inverse sqrt T) to be tested at T-2 degrees of freedom