# quant question - HELP!

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. 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. IF the calculated value is 1.71, and the DW statistic is 1.7, wouldn’t that then mean that serial correlation is present? I agree with the calculations, but i dont get the conclusion…

0 ---- L------U-------(4-U)--------(4-L)--------4 Etch the above into your memory with 2B pencil and you’ll be fine. 1.71 lies betwen U and 4-U . And it is fine. 1.7 is U.

whats this 4-U thing? able to add any more detail to this? i guess i had (erroneously) been treating DW like a plain old T test

^look at the schweser book. you need to know this.

ok, just looked at the schweser. Pain that there is more to memorize at this point… BARF

Durbin Watson test for serial Correlation or autocorrelation. For a large sample the DW = 2(1-r). R represents the correlation coefficient between the residuals in one period and the prior period. If r is positive DW is going to be less than two and if negative it will be more than two. The critical values are D1 and Du and DW < d1 positive serial correlation exist and if DW> d4 negative serial correlation exist. 0--------------2--------------4 DW < 2 positive serial corr DW>2 negative serial corr *significantly you got 1.71;personally is not significantly diff than zero.

smileygladhands Wrote: ------------------------------------------------------- > whats this 4-U thing? able to add any more detail > to this? > > i guess i had (erroneously) been treating DW like > a plain old T test This 4-U thing is not there in CFAI text, so we could skip it. Just need to know Dl and Du. One LESS complication to go thru, for a change

smiley, this is a great question, and should be mastered for the exam. In fact I’ve been wrestling with the same question for a couple months now. One core thing here is that the DW test is used to test Serial Correlation. I’m pretty sure here is how to tackle the question. 1) We know that n = 90, meaning 90 observations 2) k = 2 meaning two independent variables 3) we look at the DW table (90, 2, which is A-10 in the appendix) and we see that DW lower = 1.61, and DW upper is 1.70 4) follow me so far? 5) This is where it get’s a little tricky, but not impossible. The null is that THERE IS NOT SERIAL CORRELATION, and the alternative is that SERIAL CORRELATION EXISTS 6) 1.71 is greater than the range…SO NOW DO THE OPPOSITE OF WHAT YOUR MIND TELLS YOU TO DO, WHICH IS NORMAL T TEST THINKING. T-test says: 1.71 > critical range so I reject the null. 7) But, we’re talking about the DW, which plays by a different set of rules. If it is outside the lower and upper range, we ACCEPT THE NULL 8) We accept the null and conclude there is NO SERIAL CORRELATION To further back my hypothesis, look at #12, page 371 DW = 2(1-r) = 1.895 192 observations, so n = 192 (we use n = 100 because that is what is provided in the table) one independent variable, so k = 1 null = no serial correlation alternative = serial correlation exists DW lower = 1.65 DW upper = 1.69 DW statistic = 1.895, no refer above to steps 6,7 above ANSWER: WE FAIL TO REJECT THE NULL, AND CONCLUDE THERE IS NO POSITIVE SERIAL CORRELATION

janakisri’s post about the below graph is best to know it. 0 ---- L------U-------(4-U)--------(4-L)--------4 The other above posters gives the general rule of DW testing. To complete CFA Rhythm’s post, we fail to reject the null b/c DW 1.895 is between the 4- DW upper (2.105) and upper DW and not just because it is above the upper DW.

can you give us just a little more about the 0 ---- L------U-------(4-U)--------(4-L)--------4 please?

DW=2 is perfect because there is zero correlation . On the left side , all the way to 0 there is some probability of positive serial correlation . On the right side, all the way to 4 , there is some probability of negative serial correlation. Question is what is the probability that is “acceptable” ? Durbin-Watson ( bless them ) found that between 4-U and U ( the innermost band ) the evidence of correlation is meager and we can safely dismiss it. Between U and L ( the second band going left from the middle ) there is more probability and corrections may be needed. Think Hansen . Between U and 0 , forget it . There is very strong evidence of positive serial correlation. Same thing on negative serial side. 4-U to 4-L there is decent evidence of negative serial correlation and corrections may be needed . Think Hansen again But more than 4-L and it is curtains . There is very strong evidence of negative serial correlation.

grazie