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Asymptotic and bootstrap tests for linearity in a TAR-GARCH(1,1) model with a unit root

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  • Gospodinov, Nikolay

Abstract

This paper derives the limiting distribution of the Lagrange Multiplier (LM) test for threshold nonlinearity in a TAR model with GARCH errors when one of the regimes contains a unit root. It is shown that the asymptotic distribution is nonstandard and depends on nuisance parameters that capture the degree of conditional heteroskedasticity and non-Gaussian nature of the process. We propose a bootstrap procedure for approximating the exact finite-sample distribution of the test for linearity and establish its asymptotic validity.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 146 (2008)
Issue (Month): 1 (September)
Pages: 146-161

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Handle: RePEc:eee:econom:v:146:y:2008:i:1:p:146-161

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Threshold autoregressive model Unit root process GARCH Two-parameter Brownian motion Bootstrap;

References

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  1. Jun Yu & Peter Phillips, 2004. "Jackknifing Bond Option Prices," Econometric Society 2004 North American Winter Meetings 115, Econometric Society.
  2. Seo, Byeongseon, 1999. "Distribution theory for unit root tests with conditional heteroskedasticity1," Journal of Econometrics, Elsevier, vol. 91(1), pages 113-144, July.
  3. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-30, March.
  4. Jesús Miguel & Pilar Olave, 1999. "Bootstrapping forecast intervals in ARCH models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 8(2), pages 345-364, December.
  5. Hansen Bruce E., 1997. "Inference in TAR Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 2(1), pages 1-16, April.
  6. H. Peter Boswijk, 2001. "Testing for a Unit Root with Near-Integrated Volatility," Tinbergen Institute Discussion Papers 01-077/4, Tinbergen Institute.
  7. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(01), pages 29-52, March.
  8. Hansen, Bruce E, 1999. " Testing for Linearity," Journal of Economic Surveys, Wiley Blackwell, vol. 13(5), pages 551-76, December.
  9. Shiqing Ling & W. K. Li & Michael McAleer, 2003. "Estimation and Testing for Unit Root Processes with GARCH (1, 1) Errors: Theory and Monte Carlo Evidence," Econometric Reviews, Taylor & Francis Journals, vol. 22(2), pages 179-202.
  10. H. Peter Boswijk, 2000. "Testing for a Unit Root with Near-Integrated Volatility," Econometric Society World Congress 2000 Contributed Papers 1101, Econometric Society.
  11. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
  12. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
  13. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  14. Nikolay Gospodinov, 2005. "Testing For Threshold Nonlinearity in Short-Term Interest Rates," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(3), pages 344-371.
  15. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-96, May.
  16. Ling, Shiqing & Li, W.K., 2003. "Asymptotic Inference For Unit Root Processes With Garch(1,1) Errors," Econometric Theory, Cambridge University Press, vol. 19(04), pages 541-564, August.
  17. Francq, Christian & Zako an, Jean-Michel, 2006. "Mixing Properties Of A General Class Of Garch(1,1) Models Without Moment Assumptions On The Observed Process," Econometric Theory, Cambridge University Press, vol. 22(05), pages 815-834, October.
  18. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
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