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Testing for a Unit Root with Near-Integrated Volatility

  • H. Peter Boswijk

    (University of Amsterdam)

This paper considers tests for a unit root when the innovations follow a near-integrated GARCH process. We compare the asymptotic properties of the likelihood ratio statistic with that of the least-squares based Dickey-Fuller statistic. We first use asymptotics where the GARCH variance process is stationary with fixed parameters, and then consider parameter sequences such that the GARCH process converges to a diffusion process. In the fixed-parameter case, the asymptotic local power gain of the likelihood ratio test is only marginal for realistic parameter values. However, under near-integrated parameter sequences the difference in power is more pronounced.

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File URL: http://fmwww.bc.edu/RePEc/es2000/1101.pdf
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Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1101.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:1101
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  1. Hansen, Bruce E., 1992. "Heteroskedastic cointegration," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 139-158.
  2. repec:dgr:uvatin:19990013 is not listed on IDEAS
  3. Neil Shephard, 2005. "Stochastic volatility," Economics Series Working Papers 2005-W17, University of Oxford, Department of Economics.
  4. Hansen, Bruce E, 1995. "Regression with Nonstationary Volatility," Econometrica, Econometric Society, vol. 63(5), pages 1113-32, September.
  5. Daniel B. Nelson & Dean P. Foster, 1994. "Asypmtotic Filtering Theory for Univariate Arch Models," NBER Technical Working Papers 0129, National Bureau of Economic Research, Inc.
  6. repec:dgr:uvatin:1999013 is not listed on IDEAS
  7. repec:dgr:uvatin:2099013 is not listed on IDEAS
  8. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038 Elsevier.
  9. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
  10. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
  11. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  12. Lucas, André, 1997. "Cointegration Testing Using Pseudolikelihood Ratio Tests," Econometric Theory, Cambridge University Press, vol. 13(02), pages 149-169, April.
  13. repec:cup:etheor:v:8:y:1992:i:4:p:489-500 is not listed on IDEAS
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