Tsay's DCC model

[hashem]

dear all,

I would like to modify tsay's DCC model in example 10.5 cont(time varying correlation model).
I need to add in more series (7) as i am analysing contagion from the usa to emerging markets but i would like to filter the residuals from the regional spillovers. so the usa will be like the sp500 in the example and the other series will be the ibm series. i will modify the mean equations to add spillovers between regional emerging markets.

the probelm is i dont know how to expand correlation equation frml qf and i do not understand what the frml hf equation is?

frml qf = q0+q1*rhotv{1}+q2*u(1){1}*u(2){1}/sqrt(h{1}(1,1)*h{1}(2,2))
frml hf = hx(1,1)=hd(1),hx(2,2)=hd(2),rhotv=%logistic(qf,1.0),hx(1,2)=rhotv*sqrt(hx(1,1)*hx(2,2)),hx


regards
Hashem

[TomDoan]

HF is just a formula to return a 2x2 covariance matrix with the HD's on the diagonal and the correlation computed from the logistic index. Note that the correlation is forced into the range of (0,1) by this parameterization.

This is quite specific to a bivariate model, so I'm not sure how you would extend it to three or more.

[hashem]

how can i change the correlation so it can take any value between -1 and 1 instead of the rage(0,1)?

[TomDoan]

Instead of %logistic(qf,1.0) in the HF formula, you can use 2*%logistic(qf,1.0)-1.0