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 firstorder twostate Markov chains.
Shocks to the permanent (transitory) component take on the value Q0 (h0) if they are in a lowvolatility 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,t1=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
Markov switching regimes
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 EViews Developer
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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 bilinear 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 autocreate a specification with some of those characteristics. This can give you an idea of how to adapt these tools to your specification.
Good luck.
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 bilinear 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 autocreate a specification with some of those characteristics. This can give you an idea of how to adapt these tools to your specification.
Good luck.
Re: Markov switching regimes
Thank you Glenn, this is very helpful and much appreciated
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
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 Developer
 Posts: 2659
 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.
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
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 Developer
 Posts: 2659
 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.
I'm not entirely sure what you are saying here. Sorry.
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 Developer
 Posts: 2659
 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 residualbased statistics are (as we note in the docs):
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 nonmodeled portion). In general, the relationship is tricker here since there is an additional level of expectations taken across unknown regimes using the regime probabilities.
Of note are the residualbased statistics which employ the expected value of the residuals obtained by taking the sum of the regime specific residuals weighted by the onestep 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 nonmodeled portion). In general, the relationship is tricker here since there is an additional level of expectations taken across unknown regimes using the regime probabilities.
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