 # This is an error right...Quant Question

An 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. D) can conclude that the regression exhibits both serial correlation and heteroskedasticity.

DW is: Lower:1.61 Upper: 1.70

I think you need to do a n*r^2 of residuals and use a chi-square table to determine if there is heteroskedasticity. I don’t have a calculator or a chi-square table with me, but I could narrow the choice down to either B or C.

Can’t you calculate DW by means of 2 (1-r), i.e. 2 (1-.145)=1.71 and arrive at cannot reject null of no serial correlation because 1.71>1.70. I’m also inclined to square .145 for Breusch-Pagan but since no other info is given, C? Anyway, will call it a night…

That 2(1-r) does look eerily familiar. Quant review tomorrow for me.

Damn it, I dont get it. First off: Since 1.71 > 1.70 cant we conclude that the regression exhibits negative serial correlation. Also since nxR^2 = 90 * 0.145^2 = 1.89 which is def less than the critical value and as such cant we conclude that the regression DOESNT exhibit heteroskedasticity??? Your answer: A 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.

The DW stat is probably in the inconclusive range, would have to be bigger than 4-1.61=2.39 to have -ve correlation

if dw stat is greater than D-upper, then it’s negative serial correlation, which doesn’t affect the test.

Serial correlation: as DWstat is right after Du, you are in the “cannot reject H0” zone H0 being “No serial correlation” you cannot conclude that there is serial correlation Heteroskedasticity The correlation given in the text CANNOT be squared to get the R2 that you use in the Breusch Pagan test. They would have given us a corresponding R2 for the residuals if needed to detect any heterosked. So you cannot conclude that there is heteroskedasticity based on the information provided for

sorry disregard that post, if between 4-dl and 4 then it’s negative serial correl. but at any rate, it has to be below dl for it to be positive serial correl.