## Different cointegration vector under different regimes

Discussion of models with structural breaks or endogenous switching.

### Different cointegration vector under different regimes

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)?

nacrointfin

Posts: 9
Joined: Fri Sep 14, 2007 2:43 am

### Re: Different cointegration vector under different regimes

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.
TomDoan

Posts: 2727
Joined: Wed Nov 01, 2006 5:36 pm

### Re: Different cointegration vector under different regimes

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))?

nacrointfin

Posts: 9
Joined: Fri Sep 14, 2007 2:43 am

### Re: Different cointegration vector under different regimes

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))?

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.
TomDoan

Posts: 2727
Joined: Wed Nov 01, 2006 5:36 pm