Bruce E. Hansen and Byeongseon Seo

"Testing for two-regime threshold cointegration in vector error correction models"
Journal of Econometrics (2002), 110, 293-318.


This paper proposes a formal test for threshold cointegration and an algorithm to estimate the model parameters. Our model is a vector error correction model (VECM) with a single cointegrating vector, and a threshold effect in the error-correction term.

We propose a relatively simple algorithm to obtain maximum likelihood estimation (MLE) of the complete multivariate threshold cointegration model for the bivariate case. However, we do not provide a proof of consistency, nor a distribution theory for the MLE.

We propose testing for a threshold in this model with a Lagrange Multiplier (LM) test. This is particularly convenient since the LM test can be computed by an ordinary least squares regression involving the conventional maximum likelihood estimate of the cointegrating vector. Since the threshold is not identified under the null hypothesis, our tests take the Sup-LM form. We derive the null asymptotic distribution of the test, and find that it takes the form given in Hansen (1996). We show how to calculate asymptotic critical values by simulation. We also present a bootstrap approximation to the sampling distribution.

We investigate the performance of the test using Monte Carlo simulation, and find that the test works quite well. The Type I error of the test is quite close to the nominal level, even in a small sample with conditional heteroskedasticity.

We apply our methods to the term structure model of interest rates. In several bi-variate cointegrating VECMs, we find strong evidence for a threshold error-correction model.

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Some of the above material is based upon work supported by the National Science Foundation under Grants No. SES-9022176, SES-9120576, SBR-9412339, and SBR-9807111. Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author(s), and do not necessarily reflect the views of the NSF.