Hertroskadisticity

CFA Level II
#1

How do you test for this with autoregressive models?

#2

check out the ARCH models in the Time series chapter.

#3

Oh right it’s the ARCH test. Thanks

#4

regress the residuals of the original regression on their lagged values and check the t-stats . If they are significanr you have CH

#5

using an ARCH(1) model. Basically regress the squared error term of the original AR(1) against a lagged term. If the coefficient a1 of the lagged term is significant you have conditional heteroskedasticity.

#6

model of the form e_t^2 = a0 + a1 * e_t-1^2 check for a1=0 and look at the t-stats for that if a1 is not significantly different from 0 - then you do not have ARCH, else you have ARCH.

#7

Got it thanks - another qustion - What’s Engle granger used for?

#8

google tells me co-integration test.

#9

engle-granger is used to calculate t-stat to be used in dickey-fuller test for cointegration

#10

dickey fuller - i remember for unit root… did not see it come up with the cointegration portion

#11

thanks

#12

to test whether two time series are cointegrated Yt = bo + b1.Xt + error the residuals are tested for a unit root using DF test with critical t-values calculated by EG. If the test rejects the null hypothesis of a unit root, we conclude that the 2 time series are covariance stationary and cointegrated.

#13

CORRECTION: If the test rejects the null hypothesis of a unit root, we conclude that the error terms generated by the 2 time series are covariance stationary and time series are cointegrated.

#14

okay so wait… first you test each time series using DF-EG to see if it has a unit root. If you do not reject the null then the time series has a unit root. Assuming both time series’s have unit roots you then use yt = a + b1xt and test that series using DF-EG to see if b1=0. If you reject the null then the two time series’s are co-integrated/… RIGHT??? This is getting a bit complicated but I believe that’s right.

#15

you are correct, mambo. first you test each time series separately using DF to see if either has a unit root. If neither X nor Y has a unit root then no need to test for cointegration and you are good to go. If only one has unit root reject the model as unreliable If both have unit roots then regress Y against X and perform DF - EG as above.

#16

FINALLY got my head round this sh**. thanks man