Heteroskedasticity

CFA Level II
#1

I am a bit confused about conditional and unconditional h eteroskedasticity

Unconditional: Is this a) Error variance is not correlated with the independent variables or b) Error variance is correlated with the independent variables but not the dependent variable?

Conditional: Is this a) Error variance is correlated with the independent variables or b) Error variance is correlated with the dependent variable?

#2

  1. Unconditional heteroskedasticity means the error variance is not correlated with the independent variables , so they show an irregular behavior. The error variance could be high at the beginning to be very low at the middle and become really high at the end of the sample. That is why it is unconditional.

  2. Conditional heteroskedasticity means the error variance is correlated with the independent variables , so they show an increasing or decreasing behavior. The error variance starts to be low (high) at the beginning and becomes higher (lower) as you go through the sample. That is why it is conditional.

#3

Ok that is what I thought. So none of these include error variance correlated with the dependent variance? What would be the name of such a phenomenon?

#4

Yes, Heteroskedasticity is correlation between Independent Variables and the Error Term.

Error is expected to be correlated with the dependent variable, as we dont expect the model to explain the dependent variable 100%, and thus it is not the focus of Heteroskedasticity.

#5

Realize that the error terms are the portion of the dependent variable that couldn’t be explained by the set of independent variables. Thus, the correlation of the dependent variable and the errors is kind of useless, it does not tell much. Instead, we have R2 and adjusted R2 to tell us the portion of the variation of the dependent variable that is indeed explained by the variation of the independent variables, this is better.

One of the assumptions of linear regression is that the errors variance is constant through the whole sample. Condit. Het. violates that assumption and must be corrected using for example Hensen or robust errors. Just that.

#6

What you’ve described is _ conditional _ heteroskedasticity, not merely heteroskedasticity.

Heteroskedasticity simply means that the variance isn’t constant. It may be conditional, and it may be unconditional.

#7

True @ Magician