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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.

Suggested Citation

  • H. Peter Boswijk, 2000. "Testing for a Unit Root with Near-Integrated Volatility," Econometric Society World Congress 2000 Contributed Papers 1101, Econometric Society.
    • Handle: RePEc:ecm:wc2000:1101
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    References listed on IDEAS

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    Cited by:

    1. Boswijk, H. P. & Zu, Y., 2013. "Testing for Cointegration with Nonstationary Volatility," Working Papers 13/08, Department of Economics, City St George's, University of London.
    2. Tao, Yubo, 2019. "Limit theory for moderate deviation from Integrated GARCH processes," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 126-136.
    3. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94, Edward Elgar Publishing.
    4. 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.
    5. Anton Skrobotov, 2020. "Survey on structural breaks and unit root tests," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 58, pages 96-141.
    6. Matteo Pelagatti & Bruno Bosco & Lucia Parisio & Fabio Baldi, 2007. "A Robust Multivariate Long Run Analysis of European Electricity Prices," Working Papers 2007.103, Fondazione Eni Enrico Mattei.
    7. Joakim Westerlund, 2013. "A computationally convenient unit root test with covariates, conditional heteroskedasticity and efficient detrending," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 477-495, July.
    8. Brendan K. Beare, 2018. "Unit Root Testing with Unstable Volatility," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 816-835, November.
    9. Cavaliere, Giuseppe & Rahbek, Anders & Taylor, A.M. Robert, 2010. "Testing for co-integration in vector autoregressions with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 158(1), pages 7-24, September.
    10. Matteo Pelagatti & Bruno Bosco & Lucia Parisio & Fabio Baldi, 2007. "A Robust Multivariate Long Run Analysis of European Electricity Prices," Working Papers 2007.103, Fondazione Eni Enrico Mattei.
    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. 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," Working Papers. Serie AD 2004-11, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    13. Nikolaos Kourogenis, 2015. "Polynomial Trends, Nonstationary Volatility and the Eicker-White Asymptotic Variance Estimator," Economics Bulletin, AccessEcon, vol. 35(3), pages 1675-1680.
    14. Brandan K. Beare, 2008. "Unit Root Testing with Unstable Volatility," Economics Series Working Papers 2008-WO6, University of Oxford, Department of Economics.
    15. Vassilis Polimenis & Ioannis Neokosmidis, 2019. "Non-stationary dividend-price ratios," Journal of Asset Management, Palgrave Macmillan, vol. 20(7), pages 552-567, December.
    16. H. Peter Boswijk & Yang Zu, 2022. "Adaptive Testing for Cointegration With Nonstationary Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(2), pages 744-755, April.
    17. Nikolay Gospodinov & Ye Tao, 2011. "Bootstrap Unit Root Tests in Models with GARCH(1,1) Errors," Econometric Reviews, Taylor & Francis Journals, vol. 30(4), pages 379-405, August.
    18. 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.
    19. Peter C. B. Phillips & Jun Yu, 2024. "Information loss in volatility measurement with flat price trading," Advanced Studies in Theoretical and Applied Econometrics, in: Subal C. Kumbhakar & Robin C. Sickles & Hung-Jen Wang (ed.), Advances in Applied Econometrics, pages 501-543, Springer.
    20. 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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