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Generalized least squares estimation for cointegration parameters under conditional heteroskedasticity

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  • Helmut Herwartz
  • Helmut Lütkepohl

Abstract

In the presence of generalized conditional heteroscedasticity (GARCH) in the residuals of a vector error correction model (VECM), maximum likelihood (ML) estimation of the cointegration parameters has been shown to be efficient. On the other hand, full ML estimation of VECMs with GARCH residuals is computationally di±cult and may not be feasible for larger models. Moreover, ML estimation of VECMs with independently identically distributed residuals is known to have potentially poor small sample properties and this problem also persists when there are GARCH residuals. A further disadvantage of the ML estimator is its sensitivity to misspecification of the GARCH process. We propose a feasible generalized least squares estimator which addresses all these problems. It is easy to compute and has superior small sample properties in the presence of GARCH residuals.

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Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

Volume (Year): 32 (2011)
Issue (Month): 3 (05)
Pages: 281-291

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Handle: RePEc:bla:jtsera:v:32:y:2011:i:3:p:281-291

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  1. Peter C.B. Phillips, 1992. "Some Exact Distribution Theory for Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1039, Cowles Foundation for Research in Economics, Yale University.
  2. Saikkonen, Pentti, 1992. "Estimation and Testing of Cointegrated Systems by an Autoregressive Approximation," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 8(01), pages 1-27, March.
  3. Francis X. Diebold & Canlin Li, 2003. "Forecasting the Term Structure of Government Bond Yields," NBER Working Papers 10048, National Bureau of Economic Research, Inc.
  4. Seo, Byeongseon, 2007. "Asymptotic distribution of the cointegrating vector estimator in error correction models with conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 137(1), pages 68-111, March.
  5. E.K. Berndt & B.H. Hall & R.E. Hall, 1974. "Estimation and Inference in Nonlinear Structural Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 103-116 National Bureau of Economic Research, Inc.
  6. Hasbrouck, Joel, 1995. " One Security, Many Markets: Determining the Contributions to Price Discovery," Journal of Finance, American Finance Association, American Finance Association, vol. 50(4), pages 1175-99, September.
  7. Christian M. Hafner & Helmut Herwartz, 2009. "Testing for linear vector autoregressive dynamics under multivariate generalized autoregressive heteroskedasticity," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, Netherlands Society for Statistics and Operations Research, vol. 63(3), pages 294-323.
  8. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 11(01), pages 122-150, February.
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Cited by:
  1. Westerlund, Joakim, 2014. "On the choice of test for a unit root when the errors are conditionally heteroskedastic," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 69(C), pages 40-53.
  2. Joakim Westerlund & Paresh Narayan, 2013. "Testing the Efficient Market Hypothesis in Conditionally Heteroskedastic Futures Markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 33(11), pages 1024-1045, November.

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