The RATS Software Forum

Hi Tom and everybody:

The threhold cointegration proposed by Balke and Fomby(1997) is actually error correction that is subject to threhold effets, while the cointegration relationship is constant and linear. On the contrary,Gonzalo and Pitarakis (2006) (Gonzalo, J. and J.-Y. Pitarakis (2006). "Threshold Effects in Cointegrating Relationships*." Oxford Bulletin of Economics and Statistics 68: 813-833) allows cointegration relationship to move back and forth between regimes as a function of a threshold variable and this may be more accurate for variables such as short term and long term interest rate. Those papers applying the Gonzalo and Pitarakis (2006) model are following.
1. Krishnakumar, J. and D. Neto (2008). Testing Uncovered Interest Rate Parity and Term Structure Using Multivariate Threshold Cointegration, in Computational Methods in Financial Engineering. E. J. Kontoghiorghes, B. Rustem and P. Winker, Springer Berlin Heidelberg: 191-210.
2. Krishnakumar, J. and D. Neto (2011). "Testing Uncovered Interest Rate Parity and Term Structure Using a Three-regime Threshold Unit Root VECM: An Application to the Swiss ‘Isle’ of Interest Rates*." Oxford Bulletin of Economics and Statistics.

If I want to apply the model of Gonzalo and Pitarakis (2006), can I just run the unrestricted regression (with trheshold effects) and restricted regression (with linear relation), calculate the LM statistic and compare the LM statistic with those asymptotic critical value in Gonzalo and Pitarakis (2006)?

Any comments are welcome.

The test statistic in Gonzalo and Pitarakis can be computed using the @THRESHTEST procedure. What they've done is to provide the asymptotic distribution for that under the assumption that the y and X are cointegrated.

Hi Tom:

Thanks for your quick response. So the procedures for Gonzalo and Pitarakis (2006) are:
1. Compute the Gonzalo and Pitarakis (2006) statistic by threshrest procedure in RATS or the thr_test procedure of Hansen(2000).
2. Get the asymptotic p-value of above statistic by the pv_sup procedure of Hansen(1997)(Approximate asymptotic p-values for structural change tests." Journal of Business and Economic Statistics).
Is that correct?

Besides, in RATS is there any procedure to test for threshold effects under multivariate framework like Gonzalo and Pitarakis(2006)(Threshold Effects in Multivariate Error Correction Models. In Terence C. Mills and Kerry Patterson (eds), Palgrave Handbook of Econometrics, Volume 1: Econometric Theory (pp. 578-609))?

Thanks in advance.

nacrointfin wrote:Hi Tom:

Thanks for your quick response. So the procedures for Gonzalo and Pitarakis (2006) are:
1. Compute the Gonzalo and Pitarakis (2006) statistic by threshrest procedure in RATS or the thr_test procedure of Hansen(2000).
2. Get the asymptotic p-value of above statistic by the pv_sup procedure of Hansen(1997)(Approximate asymptotic p-values for structural change tests." Journal of Business and Economic Statistics).
Is that correct?

The @THRESHTEST procedure can compute the test statistic. The point of the paper is that the asymptotics are different in the case of cointegrated regressors.

nacrointfin wrote:Besides, in RATS is there any procedure to test for threshold effects under multivariate framework like Gonzalo and Pitarakis(2006)(Threshold Effects in Multivariate Error Correction Models. In Terence C. Mills and Kerry Patterson (eds), Palgrave Handbook of Econometrics, Volume 1: Econometric Theory (pp. 578-609))?

Thanks in advance.

Their test statistic isn't particularly difficult to compute, but I'm not sure I understand it. They're allowing the error correction matrix to vary, but are fixing the short-run matrices.

Dear Tom,
I get rejection from one of my paper investigating asymmetry in the fuel transmission channel. The main reason is the lack of nonlinear cointegration test. I have five variable VAR model. Can I apply this test to show the existence of a regime dependent cointegrating relationship.

ege_man wrote:Dear Tom,
I get rejection from one of my paper investigating asymmetry in the fuel transmission channel. The main reason is the lack of nonlinear cointegration test. I have five variable VAR model. Can I apply this test to show the existence of a regime dependent cointegrating relationship.

What type of "nonlinear cointegration test" and why was it seen as necessary?

They suggest me to use threshold a cointegration test before the application of Threshold VAR model to the first difference of the variable. But the problem is since I have a five-variable VAR model Hansen and Seo test is not applicable here. Is it possible to implement threshold cointegration test by Gonzalo and Pitarakis (2006) with RATS ?

ege_man wrote:They suggest me to use threshold a cointegration test before the application of Threshold VAR model to the first difference of the variable. But the problem is since I have a five-variable VAR model Hansen and Seo test is not applicable here. Is it possible to implement threshold cointegration test by Gonzalo and Pitarakis (2006) with RATS ?

From the abstract:

In this paper, we introduce threshold-type nonlinearities within a single equation
cointegrating regression model and propose a testing procedure
for testing the null hypothesis of linear cointegration vs. cointegration with
threshold effects. Our framework allows the modelling of long-run equilibrium
relationships that may change according to the magnitude of a threshold
variable assumed to be stationary and ergodic, and thus constitutes an attempt
to deal econometrically with the potential presence of multiple equilibria. The
framework is flexible enough to accommodate regressor endogeneity and
serial correlation.

So this is for testing for threshold cointegration vs linear cointegration. It sounds like the issue the referee has with your paper is that you ran a TVAR in differences without checking for cointegration. That would be a different issue entirely. Is there a reason to believe that the data are cointegrated? What happens when you do a standard test for that?

Yes. I applied johansen cointegration test and both trace and lambdamax test imply the existence of two cointegrating vectors. But this test is based on the assumption of linear cointegration I do not report the result just give it as a footnote.

ege_man wrote:Yes. I applied johansen cointegration test and both trace and lambdamax test imply the existence of two cointegrating vectors. But this test is based on the assumption of linear cointegration I do not report the result just give it as a footnote.

Given that cointegration tests would work the opposite way from unit root tests when it comes to the effect of threshold (recall that you accept cointegration by rejecting a unit root), if you found linear cointegration, a threshold model in differences is almost certainly misspecified. You don't need a different test---you need a different model.