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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 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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Bibliographic Info

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. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, Elsevier, vol. 45(1-2), pages 7-38.
  2. Boswijk, H. Peter & Lucas, André, 1997. "Semi-nonparametric cointegration testing," Serie Research Memoranda, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics 0041, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  3. Jurgen A. Doornik & H. Peter Boswijk, 2005. "Distribution approximations for cointegration tests with stationary exogenous regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 20(6), pages 797-810.
  4. 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.
  5. H. Peter Boswijk & Jurgen A. Doornik, 1999. "Distribution Approximations for Cointegration Tests with Stationary Exogenous Regressors," Tinbergen Institute Discussion Papers 99-013/4, Tinbergen Institute.
  6. repec:cup:etheor:v:8:y:1992:i:4:p:489-500 is not listed on IDEAS
  7. Lucas, André, 1997. "Cointegration Testing Using Pseudolikelihood Ratio Tests," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 13(02), pages 149-169, April.
  8. Neil Shephard, 2005. "Stochastic volatility," Economics Series Working Papers 2005-W17, University of Oxford, Department of Economics.
  9. repec:dgr:uvatin:2099013 is not listed on IDEAS
  10. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, Econometric Society, vol. 59(6), pages 1551-80, November.
  11. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 8(04), pages 489-500, December.
  12. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, Elsevier, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038 Elsevier.
  13. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, Econometric Society, vol. 49(4), pages 1057-72, June.
  14. Hansen, Bruce E., 1992. "Heteroskedastic cointegration," Journal of Econometrics, Elsevier, Elsevier, vol. 54(1-3), pages 139-158.
  15. Hansen, Bruce E, 1995. "Regression with Nonstationary Volatility," Econometrica, Econometric Society, Econometric Society, vol. 63(5), pages 1113-32, September.
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Cited by:
  1. Brendan K. Beare, 2008. "Unit Root Testing with Unstable Volatility," Economics Papers 2008-W06, Economics Group, Nuffield College, University of Oxford.
  2. Alvaro Escribano & Juan Ignacio Peña & Pablo Villaplana, 2002. "Modeling Electricity Prices: International Evidence," Economics Working Papers we022708, Universidad Carlos III, Departamento de Economía.
  3. Boswijk, H. P. & Zu, Y., 2013. "Testing for Cointegration with Nonstationary Volatility," Working Papers, Department of Economics, City University London 13/08, Department of Economics, City University London.
  4. H. Peter Boswijk, 2001. "Block Local to Unity and Continuous Record Asymptotics," Tinbergen Institute Discussion Papers 01-078/4, Tinbergen Institute.
  5. Peter C.B.Phillips & Jun Yu, 2008. "Information Loss in Volatility Measurement with Flat Price Trading," Working Papers, Sim Kee Boon Institute for Financial Economics CoFie-01-2008, Sim Kee Boon Institute for Financial Economics.
  6. Matteo Pelagatti & Bruno Bosco & Lucia Parisio & Fabio Baldi, 2007. "A Robust Multivariate Long Run Analysis of European Electricity Prices," Working Papers, Fondazione Eni Enrico Mattei 2007.103, Fondazione Eni Enrico Mattei.
  7. Giuseppe Cavaliere & Anders Rahbek & A. M. Robert Taylor, 2007. "Testing for co-integration in vector autoregressions with non-stationary volatility," Discussion Papers, University of Nottingham, Granger Centre for Time Series Econometrics 07/02, University of Nottingham, Granger Centre for Time Series Econometrics.
  8. 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, EconWPA 0405004, EconWPA.
  9. Bruno Bosco & Lucia Parisio & Matteo Pelagatti & Fabio Baldi, 2010. "Long-run relations in european electricity prices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 25(5), pages 805-832.
  10. Steven Cook, 2006. "The robustness of modified unit root tests in the presence of GARCH," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 6(4), pages 359-363.
  11. Xu Cheng & Peter C. B. Phillips, 2009. "Cointegrating Rank Selection in Models with Time-Varying Variance," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1688, Cowles Foundation for Research in Economics, Yale University.
  12. A. Szimayer & R. Maller, 2004. "Testing for Mean Reversion in Processes of Ornstein-Uhlenbeck Type," Statistical Inference for Stochastic Processes, Springer, Springer, vol. 7(2), pages 95-113, May.
  13. Gospodinov, Nikolay, 2008. "Asymptotic and bootstrap tests for linearity in a TAR-GARCH(1,1) model with a unit root," Journal of Econometrics, Elsevier, Elsevier, vol. 146(1), pages 146-161, September.
  14. H. Peter Boswijk & Franc Klaassen, 2005. "Why Frequency Matters for Unit Root Testing," Tinbergen Institute Discussion Papers 04-119/4, Tinbergen Institute.

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