I am writing a thesis now, and I ran into a problem - I understand the basic concepts of time series econometrics and what models and tests exist, what exactly they check, but I can not find good structured information on how to choose a model for multinomial regression. I'm looking for something like a practical guide / cheat sheet on this issue (better even without a special theory), just something with pure logic, what tests and why I do in various models (VAR/VECM/GARCH/ARIMA/HAR-RV/etc).
A very simplified example: For example, I tested with the ADF test that the regression is stationary/non-stationary. If stationary - I use VAR. If not stationary, then I check for cointegration using the Engle Granger procedure/ML estimator of Johansen. If there is no cointegration, then I take the first difference and then use VAR. If there is cointegration, I use VECM.
I really need your recommendations.