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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 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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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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  1. 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.
  2. repec:dgr:uvatin:2099013 is not listed on IDEAS
  3. Hansen, Bruce E, 1995. "Regression with Nonstationary Volatility," Econometrica, Econometric Society, Econometric Society, vol. 63(5), pages 1113-32, September.
  4. 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.
  5. H. Peter Boswijk & Jurgen A. Doornik, 1999. "Distribution Approximations for Cointegration Tests with Stationary Exogenous Regressors," Tinbergen Institute Discussion Papers, Tinbergen Institute 99-013/4, Tinbergen Institute.
  6. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  7. Daniel B. Nelson & Dean P. Foster, 1994. "Asypmtotic Filtering Theory for Univariate Arch Models," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0129, National Bureau of Economic Research, Inc.
  8. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, Elsevier, vol. 45(1-2), pages 7-38.
  9. repec:cup:etheor:v:8:y:1992:i:4:p:489-500 is not listed on IDEAS
  10. Lucas, André, 1997. "Cointegration Testing Using Pseudolikelihood Ratio Tests," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 13(02), pages 149-169, April.
  11. 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.
  12. 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.
  13. Hansen, Bruce E., 1992. "Heteroskedastic cointegration," Journal of Econometrics, Elsevier, Elsevier, vol. 54(1-3), pages 139-158.
  14. 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.
  15. H. Peter Boswijk & Jurgen A. Doornik, 1999. "Distribution Approximations for Cointegration Tests with Stationary Exogenous Regressors," Tinbergen Institute Discussion Papers, Tinbergen Institute 99-013/4, Tinbergen Institute.
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Citations

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Cited by:
  1. Peter C.B. Phillips & Jun Yu, 2007. "Information Loss in Volatility Measurement with Flat Price Trading," Levine's Bibliography 321307000000000805, UCLA Department of Economics.
  2. Cheng, Xu & Phillips, Peter C.B., 2012. "Cointegrating rank selection in models with time-varying variance," Journal of Econometrics, Elsevier, Elsevier, vol. 169(2), pages 155-165.
  3. 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.
  4. 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.
  5. Alvaro Escribano & Juan Ignacio Peña & Pablo Villaplana, 2002. "Modeling Electricity Prices: International Evidence," Economics Working Papers we022708, Universidad Carlos III, Departamento de Economía.
  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. 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.
  8. 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.
  9. 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.
  10. 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.
  11. H. Peter Boswijk, 2001. "Block Local to Unity and Continuous Record Asymptotics," Tinbergen Institute Discussion Papers, Tinbergen Institute 01-078/4, Tinbergen Institute.
  12. H. Peter Boswijk & Franc Klaassen, 2005. "Why Frequency Matters for Unit Root Testing," Tinbergen Institute Discussion Papers, Tinbergen Institute 04-119/4, Tinbergen Institute.
  13. Brendan K. Beare, 2008. "Unit Root Testing with Unstable Volatility," Economics Papers 2008-W06, Economics Group, Nuffield College, University of Oxford.
  14. 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.

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