Hi all. On p. 196 of Schweser Book 1, there is an example on the Breusch-Pagan test. The question reads: “The residual plot of mutual fund returns over time shows evidence of heteroskedasticity. To confirm your suspicions, you regress the squared residuals from the orginial regression on the set of six independent variables. The R^2 from that regression is 8%. Use the B-P test to determine whether heteroskedasticity is present.” In the answer, they take the critical value from a “chi-square distribution with one degree of freedom”, to get a critical value at a 5% significance level of 3.841. BUT! Shouldn’t there actually be 6 degrees of freedom, not 1? I thought k was the number of independent variables, per the definition on p.195? Am I right? What am I missing, if I’m wrong? Regards, Laumry (ps - Quant is HAAAARD!)
with a chi distro, df=k
Ok, now I am confused. df=k k=number of independent variables number of independent variables = 6 Then why does df not equal 6?
I saw that back when I was reading that section. I agree with you, laumry. According to the formula they provide on the page before, the degrees of freedom = k = 6 in this case. Unless I’m also confused. This isn’t posted on Schweser’s errata yet…
Why would k=6, there is only one independent variable in that in that example, mutual fund returns. n=6 in this case, not k. k=1 edit: the example is a bit misleading, it should say “over 6 observations”
ChadD Wrote: ------------------------------------------------------- > edit: the example is a bit misleading, it should > say “over 6 observations” If that is the case, then it makes sense to me.
Well stop for a moment and look at the fundamentals of the example. It’s a time series analysis of mutual fund returns over 6 time periods. So n=6, k=1. The example is a tiny bit misleading but easily solvable if you understand the scenario. I think this is key in quant. It’s easy to try to scan the problem and find n or k but that can often lead to mistakes. You need to pause and examine the scenario not just pick out numbers to fill the formulas.
All - thanks for the advice! Regards, laumry
Whoa… 1) Knowing that your test statistic is a chi-square gives you no information at all about the d.f. that you should use. 2) The Breusch Pagan test in this case (and all cases) has one dependent variable - the squared residuals. In this case it has 6 independent variables. They do not tell you what they are in this case but they are probably not time. Imagine regressing equity mutual fund returns on oil returns, interest rate changes, etc… 3) The test statistic is based on k-1 d.f. = 5 here, not 6 or 1. 4) " It’s a time series analysis of mutual fund " - Nope it’s a standard regression analysis