I want to build some kind of two-stage Markov switching model but with two time-series. My general idea was to calculate some kind of dependence between two time-series in two different periods of time. For example, GNP and inflation in a period from 2000 till 2010. Let' assume that they were positively correlated between 2000 and 2005 and after the year of 2005 - negatively correlated. Maybe Markov switching can help me but I am very new to it.
Standard Hamilton model operates only one time series finding regimes. But if we want to find any regime between two of them? Let's assume (just for an example) we want to find regimes in equations like:
*DLOGGNP=C(1)*DLOGCPI + C(2) + [AR(1)=C(5)];
*DLOGGNP=C(3)*DLOGCPI + C(4) + [AR(1)=C(5)]
1)Can we use Markov switching in that example(to find regimes between some period of 2 series)?
2)Can we use AR model in that example?
3) This video describes that model in Eviews https://www.youtube.com/watch?v=0nciNxV0xZ4
Is it right? Can we use dependent and independent variables in order to build Markov switching between two time series (GNP and CPI, in video g and GPN)?