[R] Doing time series markov regime switching in R

[Maxim Fomin]

Dear all,

I am doing business cycle research on industry data. One of methods to identify
cycle is Markov regime switching. As I see, there is a MSwM package
for the purposes which is pretty straightforward to use. However, some
questions for me remain:

1) Are there any packages? This is relevant because I could not couple
with 2-3-4.
2) The MSwM package provides example for regression analysis (one of
the steps is to provide regression model to msmFit). In my case I have
time series. Googling issue shows that regressing on intercept is
sufficient (i.e. 'time_data ~ 1') but I am not sure.
3) The package provides some diagnostic tools, mainly plotDiag (shows
pooled residuals, QQ plot, residual acf). However, it does not provide
tools to test a) that intercepts are same b) state variables are
independent. Accepting respective null hypotheses is evidence against
the model. How this can be done in R?
4) The package allows AR terms to be affected by unobservable state
's' through 'p' parameter. However, it is unclear when specification
should include switching in coefficients (ok, it depends on use case,
but what is general theory?).

Thanks in advance,
Best regards.