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Testing for a Unit Root with Near-Integrated Volatility

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  • H. Peter Boswijk

    () (University of Amsterdam)

Abstract

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 both cases, we find a substantial asymptotic local power gain of the likelihood ratio test for parameter values that imply heavy tails in the unconditional innovation distribution. An empirical application to the term structure of interest rates in the Netherlands illustrates the proposed procedures.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 01-077/4.

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Date of creation: 23 Aug 2001
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Handle: RePEc:dgr:uvatin:20010077

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References

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  1. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
  2. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  3. 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.
  4. repec:cup:etheor:v:8:y:1992:i:4:p:489-500 is not listed on IDEAS
  5. 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.
  6. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  7. Hansen, Bruce E, 1995. "Regression with Nonstationary Volatility," Econometrica, Econometric Society, vol. 63(5), pages 1113-32, September.
  8. 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.
  9. Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January.
  10. Hansen, Bruce E., 1992. "Heteroskedastic cointegration," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 139-158.
  11. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
  12. Boswijk, H. Peter & Lucas, Andre, 2002. "Semi-nonparametric cointegration testing," Journal of Econometrics, Elsevier, vol. 108(2), pages 253-280, June.
  13. Lucas, André, 1997. "Cointegration Testing Using Pseudolikelihood Ratio Tests," Econometric Theory, Cambridge University Press, vol. 13(02), pages 149-169, April.
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Citations

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Cited by:
  1. Paulo M. M. Rodrigues & Antonio Rubia, 2004. "On the Small Sample Properties of Dickey Fuller and Maximum Likelihood Unit Root Tests on Discrete-Sampled Short-Term Interest Rates," Econometrics 0405004, EconWPA.
  2. Steven Cook, 2006. "The robustness of modified unit root tests in the presence of GARCH," Quantitative Finance, Taylor and Francis Journals, vol. 6(4), pages 359-363.
  3. Alvaro Escribano & J. Ignacio Peña & Pablo Villaplana, 2011. "Modelling Electricity Prices: International Evidence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 73(5), pages 622-650, October.
  4. H. Peter Boswijk & Franc Klaassen, 2005. "Why Frequency Matters for Unit Root Testing," Tinbergen Institute Discussion Papers 04-119/4, Tinbergen Institute.
  5. Giuseppe Cavaliere & Anders Rahbek & A. M. Robert Taylor, 2008. "Testing for Co-integration in Vector Autoregressions with Non-Stationary Volatility," Discussion Papers 08-34, University of Copenhagen. Department of Economics.
  6. Peter C. B. Phillips & Jun Yu, 2009. "Information Loss in Volatility Measurement with Flat Price Trading," Global COE Hi-Stat Discussion Paper Series gd08-039, Institute of Economic Research, Hitotsubashi University.
  7. Xu Cheng & Peter C. B. Phillips, 2009. "Cointegrating Rank Selection in Models with Time-Varying Variance," Cowles Foundation Discussion Papers 1688, Cowles Foundation for Research in Economics, Yale University.
  8. Gospodinov, Nikolay, 2008. "Asymptotic and bootstrap tests for linearity in a TAR-GARCH(1,1) model with a unit root," Journal of Econometrics, Elsevier, vol. 146(1), pages 146-161, September.
  9. Brendan K. Beare, 2008. "Unit Root Testing with Unstable Volatility," Economics Papers 2008-W06, Economics Group, Nuffield College, University of Oxford.
  10. H. Peter Boswijk, 2001. "Block Local to Unity and Continuous Record Asymptotics," Tinbergen Institute Discussion Papers 01-078/4, Tinbergen Institute.
  11. Bruno Bosco & Lucia Parisio & Matteo Pelagatti & Fabio Baldi, 2010. "Long-run relations in european electricity prices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(5), pages 805-832.
  12. A. Szimayer & R. Maller, 2004. "Testing for Mean Reversion in Processes of Ornstein-Uhlenbeck Type," Statistical Inference for Stochastic Processes, Springer, vol. 7(2), pages 95-113, May.

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