The RATS Software Forum

Hi everyone,

I am building a time series model with 3 KNOWN regimes. The idea is to check whether the impact from explanatory variables are different for different regimes. I am thinking about using 2 dummies to catch the different impact of explanatory variables on my dependent variable as follows:

y(t) = C0 + C1*y(t-1) + C2*x(t-1) + C3*D(1) + C4*(D(1)*y(t-1)) + C5*(D(1)*x(t-1)) + C6*(D(2)*y(t-1)) + C7*(D(2)*x(t-1))

Cs are the coefficients, Ds are the dummies. y and x are time series with one unit root - I(1)s.

Could anyone has some experience tell me whether this approach is workable and suggest some RATS codes for this?

Or any better ways to model this?

thank you very much in advance,
anozman

You are probably going to have to be more careful about the specification of that model. As written, you can't just run that and do F-tests because the F's will have non-standard distributions as they'll be tests on non-stationary variables. If x and y aren't cointegrated, the coefficients on x would have to be zero if the residual is stationary.

Hi Tom,

Thanks for the reply. The residuals are stationary , suggesting it is a cointegrating model. Of cause, the lags of each Xs are different for different regimes of Ds. Would F- or X^2 test still be an issue? The model passes all usual time series tests, such as non auto correlation, no arch effects and normality, etc.

Many thanks,
Anozman

Whether the variables are cointegrated or not, the test for the different regimes has a non-standard distribution. This is the Sims-Stock-Watson result. In your case, the regimes could have different coefficients because the cointegrating vectors are the same, but the loadings aren't, or the cointegrating vectors could be different. The second is a long-run property and the first isn't. It sounds like you haven't examined the cointegration properties of your data, and you really need to do that before going forward.

many thanks Tom for your suggestions, anozman

Hi Tom,

What do you mean by the cointegration property in the previous post and what did you propose to test? I have read some material on this and am still a bit confused about this? Is Pesaran et al 2001's simulated critical values for level relationship relevant to this problem?

Many thanks,
Anozman

Hi Tom,

Please find the attached reference paper - Pesaran et al 2001.

Many thanks,
Anozman

anozman wrote:Hi Tom,

What do you mean by the cointegration property in the previous post and what did you propose to test? I have read some material on this and am still a bit confused about this? Is Pesaran et al 2001's simulated critical values for level relationship relevant to this problem?

Many thanks,
Anozman

It's your data and it's your model. You brought up that the variables were I(1). If the data aren't cointegrated, given the construction of your model, the C2, C5 and C7 would have to be zero (in theory). If you had extra lags on X, it would no longer be the case that the coefficients on lags of X would be theoretically zero (as the lag coefficients could, in effect, difference out the unit root), however, that would make your basic hypothesis unworkable.

The Pesaran paper doesn't apply because it's a test for the exclusion of the full lagged "X", not for shift dummies x X leaving the base contribution intact.

Hi Tom,

Thank you very much for your feedback.

Anozman