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I would probably help if I knew exactly what you need guidance with. look up HAMILTON 1989 paper on regime switching time series. He pioneered that idea and provided a decent filter for estimation of switching time series. I haven't worked on switching Garch yet but I bet the model has been...

Hey Caroll I am in a similar situation. I got a Master in applied mathematics with emphasis in finite difference treatment of PDEs. I've just been offered admission in a couple of Phd programs in stat. I will sit for the qualifying examinations a week after the beginning of the fall semester. I...