TAR/STAR Example

[TomDoan]

The following is an example with both TAR (sharp cutoff) and STAR estimation. This is based on example 4 from Terasvirta(1994), "Specification, Estimation and Evaluation of Smooth Transition Autoregressive Models", JASA, vol 89, pp 208-218. The TAR estimation was added to that.

Both TAR and STAR pick the 4th lag as the best indicator. The TAR model, however, doesn't show strong evidence of a threshold effect on bootstrap simulations. The LM test for STAR does. When estimated, however, the STAR also doesn't show that strong a threshold effect; the behavior of the two branches isn't that different.

tarmodels.rpf

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Data file:

ger4ind.prn

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[nbcheikh]

Hello,
Can we apply Terasvirta(1994) example in a multivariate case, such y_t = a1.y_(t-1)+a2.x_(t)+a3.x(t-2)...?
Especially, how can we modify startest.src in order to test linearity vs STAR model in such case ?
Thanks

[TomDoan]

Hello,
Can we apply Terasvirta(1994) example in a multivariate case, such y_t = a1.y_(t-1)+a2.x_(t)+a3.x(t-2)...?
Especially, how can we modify startest.src in order to test linearity vs STAR model in such case ?
Thanks

The auxiliary variables for the test would include not just the interactions between powers of y{d} with the included lags of y from the regression, but also the interactions of the powers of y{d} with the included exogenous variables.

[nbcheikh]

Thank you for your reply,
But startest.src is designed to univariate case (such as @startest y 1990:1 2009:12), how can I include the other regressors in this procedure ? or is there anoher method to run this test with multiple regressors ?
Thank you

[TomDoan]

All that STARTEST does is to generate a specific set of regressors for an auxiliary regression (residuals on original regressors + extra variables). You just have to generate the required regressors yourself, run the regression and test the significance of the added variables.

[nbcheikh]

Thank you. It works very well.
The final step in Terasvirta (1994) (evaluation stage), the estimated STAR model needs to be evaluated before it can be used for forecasting or other purposes, so how can we do misspecification tests (especially "no additive linearity" or "parameter constancy") with RATS ?

[TomDoan]

The constancy test can be done using the @FLUX procedure. Most LM tests will be done using the same VECT[SERIES] of derivatives needed for using @FLUX. You either regress the residuals on the derivatives + auxiliary variables, or use MCOV with the OPGSTAT option to get the test statistic.