Reading 13, LOS 13.L

Hi there. I’m having trouble conceptualizing the concept of autoregressive conditional heteroskedasticity. per the LOS, “discuss how ARCH models can be applied to predict the variance of a time series.” I’ve read the curriculum a couple times. Seems like a lot of mumbo jumbo. Will someone please break this down? Also, how many dof do we use when testing for seasonality? Is it always n-2?

looking at a time series model, we assume that the error term’s variance is constant and not dependent on the independent variable (homoskedasticity). if you have an AR model and heteroskedasticity (when the variance of the residuals is NOT the same across all observations) exists, the std errors of the regression coefficients of the model are going to be incorrect, and one of your terms might appear statistically significant when it’s not… your results are not going to be accurate. So ARCH from what I understand is a way of testing whether the variance of the error term in a time series model in 1 period depends on the variance of the error in past periods- when the variance of the error in a time series model does depend on the variance of previous errors, this represents ARCH. We can test for ARCH by regressing the sq residuals on the sq residual from a previous period. we predict the variance of the errors in period t+1 using period with that formula that’s on pg 396 of the CFA materials. they then show an example on the next page or 2 of how to predict the variance from the stats if they give you some statistical results. for the 2nd question and someone correct me if i’m wrong, i think it would be the n - (k+1), so in the example they use with just sales, it does wind up being n - 2. maybe this doesn’t help much… i am not sure that they’d get too crazy maybe on the test with a problem involving this all- maybe just looking at data and identifying that there’s ARCH there or using that formula to predict variance in t+1? if anyone’s taken L2 and can offer insight, awesome. i hope this isn’t too heavily tested! i haven’t jumped into qbank yet also to see what kinds of quant problems we’re going to be looking at. i probably should do that more as i take a 1st read over everything.

I hope your assessment is right about how they’ll test this, if at all. Thank you for your reply. I laugh at myself because even after reading over your well articulated pose, I’m still fuzzy with this concept. It must be the low aptitude kicking in. Has anyone here actually applied this analysis in real life?

joey stat-man help us? no, i haven’t done much of any of this in real life! i think that for this l2 quant so far, it has been a lot of big words that i’ve had to read back many times to even start to understand. i did the CFA end of chapter problems and the schweser end of chapter problems- i should try to reinforce w/ qbank. i started on FI this weekend… it’s been much less painful and easier to read so far (i’m in schweser SS14, pretty basic FI stuff).