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Testing for a Unit Root with Near-Integrated Volatility

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Author Info
H. Peter Boswijk () (University of Amsterdam)

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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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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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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
  2. Boswijk, H. Peter & Lucas, Andr‚, 1997. "Semi-nonparametric cointegration testing," Serie Research Memoranda 0041, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics. [Downloadable!]
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  3. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38. [Downloadable!] (restricted)
  4. repec:cup:etheor:v:8:y:1992:i:4:p:489-500 is not listed on IDEAS
  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. [Downloadable!]
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  6. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  7. Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January. [Downloadable!] (restricted)
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  8. Hansen, Bruce E., 1992. "Heteroskedastic cointegration," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 139-158. [Downloadable!] (restricted)
  9. Tim Bollerslev & Robert F. Engle & Daniel B. Nelson, 1993. "ARCH Models," University of California at San Diego, Economics Working Paper Series 93-49, Department of Economics, UC San Diego. [Downloadable!]
    Other versions:
    • 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. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
  11. Hansen, Bruce E, 1995. "Regression with Nonstationary Volatility," Econometrica, Econometric Society, vol. 63(5), pages 1113-32, September. [Downloadable!] (restricted)
  12. Lucas, Andr?, 1997. "Cointegration Testing Using Pseudolikelihood Ratio Tests," Econometric Theory, Cambridge University Press, vol. 13(02), pages 149-169, April. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!]
    Other versions:
  2. 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. [Downloadable!]
    Other versions:
  3. H. Peter Boswijk, 2001. "Block Local to Unity and Continuous Record Asymptotics," Tinbergen Institute Discussion Papers 01-078/4, Tinbergen Institute. [Downloadable!]
  4. 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. [Downloadable!] (restricted)
  5. Brendan K. Beare, 2008. "Unit Root Testing with Unstable Volatility," Economics Papers 2008-W06, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  6. 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, August. [Downloadable!] (restricted)
  7. H. Peter Boswijk & Franc Klaassen, 2005. "Why Frequency Matters for Unit Root Testing," Tinbergen Institute Discussion Papers 04-119/4, Tinbergen Institute. [Downloadable!]
  8. Álvaro Escribano & Juan Ignacio Peña & Pablo Villaplana, 2002. "Modeling Electricity Prices: International Evidence," Economics Working Papers we022708, Universidad Carlos III, Departamento de Economía. [Downloadable!]
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