## Cai SWARCH model

Discussion of models with structural breaks or endogenous switching.

### Cai SWARCH model

Hello,

I try to replicate the Cai model of Markov switching ARCH. The SWARCH.rpf is based on this model. It was not a problem to change it to the two state model. However, in the Cai model, the formula is not just u(t)=(y-mu), but u depends on the state variable as well as on lagged values of u. Thus, the FRML statement (at the end of UG-369) has to be modified. But at this point I am lost somewhat. I changed the FRML statement to

frml logl = u(t)=(x-c0-c1*%if(pstar(1)<0.5,1,0)-b1*temp{1}), temp=u(t),uu(t)=u(t)^2,f=ARCHStateF(t,u(t)),\$
pt_t1=%mcstate(p,pstar),pt_t=pstar=%msupdate(f,pt_t1,fpt),log(fpt)

I have defined and initialized the parameters, c0,c1 and b1 and set the temp series to 0.0 before the frml statement is executed. Running the modified SWARCH program leads to the no conversion statement. Is it logical mistake that I made or is it just the data which leads to no result for the maximization?

Best regards
Peter
PeterF

Posts: 10
Joined: Thu Apr 12, 2012 2:03 pm

### Re: Cai SWARCH model

The Dueker SWARCH/SWGARCH models also include a switching mean: http://www.estima.com/forum/viewtopic.php?f=8&t=1190. His SWARCH uses the Hamilton-Susmel form rather than Cai, but the handling of the switching mean model would be the same either way.
TomDoan

Posts: 2724
Joined: Wed Nov 01, 2006 5:36 pm

### Re: Cai SWARCH model

Tom,

thanks a lot for the very quick help
PeterF

Posts: 10
Joined: Thu Apr 12, 2012 2:03 pm

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