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Testing for a Unit Root with Near-Integrated Volatility

  • Boswijk, H.P.

    ()

    (Universiteit van 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 likelihoodratio statistic with that of the least-squares based Dickey-Fuller statistic. We first useasymptotics where the GARCH variance process is stationary with fixed parameters,and then consider parameter sequences such that the GARCH process converges to adiffusion process. In both cases, we find a substantial asymptotic local power gain ofthe likelihood ratio test for parameter values that imply heavy tails in theunconditional innovation distribution. An empirical application to the term structureof interest rates in the Netherlands illustrates the proposed procedures.

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File URL: http://cendef.uva.nl/binaries/content/assets/subsites/amsterdam-school-of-economics-research-institute/cendef/working-papers-2000/urnivol.pdf?1417178388071
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Paper provided by Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance in its series CeNDEF Working Papers with number 00-09.

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Date of creation: 2000
Date of revision:
Handle: RePEc:ams:ndfwpp:00-09
Contact details of provider: Postal:
Dept. of Economics and Econometrics, Universiteit van Amsterdam, Roetersstraat 11, NL - 1018 WB Amsterdam, The Netherlands

Phone: + 31 20 525 52 58
Fax: + 31 20 525 52 83
Web page: http://www.fee.uva.nl/cendef/
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  1. repec:cup:etheor:v:8:y:1992:i:4:p:489-500 is not listed on IDEAS
  2. Jurgen A. Doornik & H. Peter Boswijk, 2005. "Distribution approximations for cointegration tests with stationary exogenous regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(6), pages 797-810.
  3. Lucas, André, 1997. "Cointegration Testing Using Pseudolikelihood Ratio Tests," Econometric Theory, Cambridge University Press, vol. 13(02), pages 149-169, April.
  4. Hansen, Bruce E, 1995. "Regression with Nonstationary Volatility," Econometrica, Econometric Society, vol. 63(5), pages 1113-32, September.
  5. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  6. Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January.
  7. 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.
  8. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  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. Hansen, Bruce E., 1992. "Heteroskedastic cointegration," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 139-158.
  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. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
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