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. In case you don’t have your DW table handy- the lower/upper is 1.61-1.7 for this problem.
Damn. I have nothing with me here but I hate the fact that I just don’t KNOW this one. I should. I guess there’s no serial correlation nor heteroskedasticity. So C?
DW = 2 * (1-r) = 1.71 This is above Upper DW value so do not reject Ho of no serial correlation so no serial correlation so B or C regarding heteroskedasticity, we are not given the R squared of residuals…so I would go with cannot conclude So C also?
C - I didn’t look at the DW table, but 1.71 probably falls into the inconclusive zone.
d is approximately 2(1-r)=1.71 for large n. So evidence that not serially correlated, and no information there regarding heteroskedasticity. C edit: Too slow!
The question is too difficult - I’ll go with A ??? correlation = 0.145 n = 90 k=2 (1real + 1dummy) R^2 = r^2 R^2 = 0.021025 DW(stat) = 2(1-r) = 1.71 DW(90,2,0.05) -> du =1.61 dl=1.70 1.71 > 1.70: Do not reject Null: Hence (Positive) Serial Corelation present??? BP Test = 90*(0.021025) = 1.89225 BP(Chi[2, 0.025]) = 7.378 1.89225 < 7.378 Fail to reject Null. Thus -> No CH
C. D_u< DW < 4-D_u Do not reject null: so no serial correlation. Can’t conclude about the Conditional Heteroskedasticity either. no way to conduct the BP test. BP test is the n * R^2. R^2 here’s the coefficient of determination for the independent variable towards the error term. You can’t just square up the correlation here. totally different things.
Nice work team! My dumb question (too lazy to dig into the books)- what does it mean when the DW stat is either lower than the lower number, in between, or higher than the upper. pos/neg serial correlation, inconclusive, can someone just lay me out a 2 second cheat sheet of what the DW stat means when it’s outside or inside the zones? i guessed right… but would rather not have to guess on the DW side. Your answer: C was correct! 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.
c
picture this: _________L____________U_______4-U____________4-L________ *POSITIVE**INCONCLUSIVE**NULL OK**INCONCLUSIVE***NEGATIVE To simplify, just remember this: _________L___________________________________4-L________ *POSITIVE********ACCEPT NULL HYPOTHESIS***********NEGATIVE
lxwqh - you almost did a brilliant job of explaining this, but the format got messed up. Could you try again. It would be of great help to us. Thanks! EDIT: Thanks lxwqh - that was helpful.
so we’d be anthing under 1.6 = pos correlation here, 1.6 to 1.7 inconclusive, 1.7 to 2.3 kool and the gang, 2.3 to 2.4 inconclusive, 2.4 and higher neg serial corr. so we fall in the ok area. even if we fell inconclusive we wouldn’t say for sure serial correlation. SUH-WEET thank you this is EXACTLY what I knew this group would give me.
lxwqh Wrote: ------------------------------------------------------- > picture this: > > _________L____________U_______4-U____________4-L__ > ______ > *POSITIVE**INCONCLUSIVE**NULL > OK**INCONCLUSIVE***NEGATIVE > > To simplify, just remember this: > > _________L___________________________________4-L__ > ______ > *POSITIVE********ACCEPT NULL > HYPOTHESIS***********NEGATIVE I think the simplyfing approach would not work because there is a difference between inconclusive and no correlation. With no correlation, you know for sure that there is no serial correlation. In the inconclusive range, you don’t know if it is or not.
technically, you are right. but for exam; as long as the DW falls in the range [L, 4-L]; you can’t reject the null hypothesis. ideally, remember the whole thing which is not too bad.
I understand what you mean. It is a good simplifier 