ARCH

[brazilatz]

I can’t seem to understand what is an ARCH model… Can anybody explain this in an easy way? Tks.

 

[idreesz]

There is no easy way to understand. Either you get it or you dont.
I have read it a total of 3 times till now and I still dont get it.

 

[janakisri]

Conditional Heteroskedasticity is a serious problem which can invalidate a regression model results . ARCH attempts to study if past variance is correlated to current variance i.e.
Remember that the et terms are the residuals from the ORIGINAL AR(1) model !
Create a new variable which is THE residuals from the ORIGINAL AR(1) model.
Then do a regression study on this variable unto itself :
et^2 = b0 + b1et-1^2 + errort
If this new model shows a high degree of correlation , i.e. high t-stats , then the ORIGINAL model is ARCH(1)
Do you then toss it out?
Well , maybe you can use it to predict variance one period out , although I find this somewhat fishy , since if you can predict variance on the basis of a faulty model , then why is the original model fauly?
Ah well , that’s just the way it is , put a spin on it , and then try and sell a new idea , that’s what quant is about I think , selling normal distributions around even tho tail events regularly invalidate the norm big tme

 

[job71188]

What ARCH tests is if there is conditional heteroskedasticity which is when error terms are correlated with each other. Looking at a graph is the best way to grasp what conditional heteroskedasticity is.
Basically, ARCH is used to see if conditional heteroskedasticity. How ARCH does this, is it runs a regression with the Error Term at period x as the dependent variable. The independent variavble is Error Term at period x-1.
So it is basically testing how good last period’s error term is at predicting this period’s error term. If the regressoin is significant and last period’s error term does a good job predicting this period’s error term, conditional heteroskedasticity is present.
If the test is insignificant, then the error term at x-1 does a poor job at predicting the error term at period x. In this case, the error term is random and no heteroskedasticity is present.
It’s actually a pretty smart way to test for this problem when you think about it. You basically run a regression on the lagged error terms of your original regression against the error terms of your original regression.

 

[adee1031]

I remember learning the Breusch-Pagan (nR^2) to test conditional heteroskedasticity, is ARCH another alternative?
Also one question i did said to use Generlized Least Square to correct ARCH. Can someone please explain this?

 

[the show NY]

Linear regression:
Issue: Conditional H, which means variance of residuals is nonconstant and and related to independent variables
Detect Conditional H: BP test
Correct Condition H: Robus standard errors
Time series regression:
Issue: ARCH, which means variance of residuals in one period are dependent on variance of residuals in previous period.
Detect ARCH: test if coefficient a1 is stat sig different from zero
Correct ARCH: generalized least squares
Although not completely correct, you can think of ARCH as simply Condition H for a time series model.