Is stationarity assumption needed for a switching model?

[anozman]

Hi all,

I was wondering whether someone could help me to understand if stationarity assumption is needed for both dependent and independent variables to estimate a single equation switching model?

many thanks,
anozman

[TomDoan]

No. They don't have to be stationary.

[anozman]

Thanks for your quick reply. Do that mean as long as the standardised residuals is a stationarity process, then the resultant switching model is valid?

Many thanks,
Anozman

[TomDoan]

Thanks for your quick reply. Do that mean as long as the standardised residuals is a stationarity process, then the resultant switching model is valid?

Many thanks,
Anozman

MS models rely upon something quite a bit stronger than "stationary" residuals---the assumption is that the true residuals (if the regime were known) are independent and Normal. Because the regime isn't known, that's not really a testable hypothesis. About all you can really test is whether the standardized residuals are uncorrelated and constant variance. Note that passing those tests doesn't make the model "valid", just not rejectable.

[anozman]

Many thanks Tom for your help. I really appreciate it!

Anozman

[anozman]

Hi Tom,

If I have a model with two regimes and the variance follows a GARCH model, do you know what kind of assumptions it needs to meet?

many thanks
anozman

[TomDoan]

That it has two regimes and the variance follows a GARCH process with a known conditional distribution.

However, those are very complicated models.

[anozman]

Hi Tom,

Do you mean the standardised residuals need to follow a known conditional distribution?


Anozman

[TomDoan]

I'm sorry. What do "standardized residuals" have to do with this? MS models require that conditional on the parameters, the past data and the current regime (treated as known), the data at t have a known likelihood. You can have MS probit models, which don't have "residuals" standardized or not. For a MS GARCH model, you need the data to be conditionally Normal (typically, though t is possible) with a GARCH variance process. MS GARCH models aren't complicated conceptually---they're complicated to estimate because the variance isn't observable.

[anozman]

HiTom,,

Could you please tell me how to determine the lag length of each variables and the number of regimes in a single equation MS-model? In addition, what is the RATS sample code for checking these? I have the MS model course material, but it does not talk much about these. Alternatively, could you suggest any books that are excellent references for MS-model buliginbuilding?

Best regards,
Anozman

[TomDoan]

Lag length can be chosen using standard methods (BIC or AIC), though because of the complication of getting MS models to fit, it usually makes sense to pick a reasonable number and see if there is any indication that it's clearly too high or low (insignificant coefficients or serially correlated standardized residuals). There's no simple way to do the number of regimes. Basically, you have to fit the model with additional regimes and see if it works---if additional regimes aren't necessary, the expanded model isn't identified.

Is there a particular reason that you think you need a MS model? Even quite a bit of published work with MS models is rather unpersuasive about the need for a MS model.

[anozman]

Hi Tom,

The objective is to investigate the impact of a few variables on one risk indicator during different time periods and different economic environment. For example, MS models will show different coefficients for different periods, confirming different impacts of a variable. Do you think there are much better modelling techniques that can be used to answer this research question and are much easier to apply?

Best regards,
Anozman

[TomDoan]

Markov switching models have two or more regimes governed by an unobservable switching process. That means they can switch from one to the other and back at any time. If the changes would be based upon time period or are a once-and-for-all-change, that's not Markov. Because the Markov process isn't unobservable, you can only guess as to what each regime "means"---one of the problems with much published empirical work is that the model doesn't really support the desired interpretation of the regimes.

[anozman]

Hi Tom,

Do you know how to deal with multicollinearity problem in MS models?

Regards,
Anozman

[TomDoan]

What multicollinearity problem?