## Markov switching regimes

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vasco1966
Posts: 3
Joined: Fri Aug 23, 2019 5:55 am

### Markov switching regimes

Hi:

I am trying to estimate the following Markov Switching model of regime heteroskedastic:

inflation in time t = trend inflation + U2S1,t + U3S2,t + U4S1,t S2,t + (h0 + h1S2,t)Nt

where trend inflation = trend inflation(-1) + (Q0 + Q1S1,t)Et

Here, Si,t = unobserved state variable that represents the regime shift. Both S1,t and S2,t are assumed to evolve according to 2 independent first-order two-state Markov chains.

Shocks to the permanent (transitory) component take on the value Q0 (h0) if they are in a low-volatility state and Q0+Q1 (h0+h1) otherwise.

My question is this: how do you include the state variables into the equation to be estimated? How do you define the state variables (S1,t=0 given S1,t-1=0, etc) so that they can be included as regressors? Should the trend inflation equation be included as probability regressors?

Any guidance will be greatly appreciated

EViews Glenn
EViews Developer
Posts: 2658
Joined: Wed Oct 15, 2008 9:17 am

### Re: Markov switching regimes

Two things.

First, it's a little hard to read the notation so I may be misunderstanding what you are trying to do. If so, apologies in advance.

Second, if I am understanding correctly, you have a specification that is bi-linear in the states, with the product of the two state variables entering into the observables equation. Note that this doesn't follow the standard form of the linear state space model and cannot be estimated using our tools.

As to the specific question, you simply define new state variables using the @state keyword, and then enter those variables into the observables equation. The manual has examples. Also, you can use the Proc for specifying a state space model to auto-create a specification with some of those characteristics. This can give you an idea of how to adapt these tools to your specification.

Good luck.

vasco1966
Posts: 3
Joined: Fri Aug 23, 2019 5:55 am

### Re: Markov switching regimes

Thank you Glenn, this is very helpful and much appreciated

Posts: 30
Joined: Sat Dec 05, 2009 5:56 pm

### Re: Markov switching regimes

HI. I've estimated a model using MC regime switching method. Did it because VIX, which is an explanatory variable in the model, shows structural breaks, i.e., high and low volatility. My output table shows the results for the two regimes and I have the estimates of the log( sigma).

Question: It isn't clear to me which regime is associated with high volatility readings of VIX and which with low? I'm assuming that the high log (sigma) is associated with high volatility and low log (sigma) with low? Not sure though. I hope this is clear. Any help is appreciated. Thanks much. Best, BA

EViews Glenn
EViews Developer
Posts: 2658
Joined: Wed Oct 15, 2008 9:17 am

### Re: Markov switching regimes

The sigma are the standard errors of the dependent variable, not of the explanatory variables (e.g., VIX). Not sure if this answers your question.

Posts: 30
Joined: Sat Dec 05, 2009 5:56 pm

### Re: Markov switching regimes

Thanks. The output only says regime 1 and 2. Not clear what these regimes are.

I thought the sigma of the dependent variable is the sigma of the innovations (residuals) of the model. Therefore, the values of the sigma should reflect the impact of the structural breaks of VIX on the dependent variable, and through that on the innovations. Thoughts? Thanks. BA

EViews Glenn
EViews Developer
Posts: 2658
Joined: Wed Oct 15, 2008 9:17 am

### Re: Markov switching regimes

Sorry, didn't see this until now.

I'm not entirely sure what you are saying here. Sorry.

Posts: 30
Joined: Sat Dec 05, 2009 5:56 pm

### Re: Markov switching regimes

Thanks. What I mean is that the variance of residuals is normally the variance of dependent variable in all regressions. So should be the same here, shouldn't it? Thanks. BA

EViews Glenn
EViews Developer
Posts: 2658
Joined: Wed Oct 15, 2008 9:17 am

### Re: Markov switching regimes

Still not sure that I understand. What we are computing as residuals and using for residual-based statistics are (as we note in the docs):

Of note are the residual-based statistics which employ the expected value of the residuals obtained by taking the sum of the regime specific residuals weighted by the one-step ahead (unfiltered) regime probabilities (Maheu and McCurdy, 2000).

I am still unclear as to how you think the variance of the residuals is related to the variance of the dependent variable (other than being the non-modeled portion). In general, the relationship is tricker here since there is an additional level of expectations taken across unknown regimes using the regime probabilities.