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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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  • 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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    Cited by:

    1. Boswijk, H. P. & Zu, Y., 2013. "Testing for Cointegration with Nonstationary Volatility," Working Papers 13/08, Department of Economics, City University London.
    2. 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.
    3. Peter C. B. Phillips & Jun Yu, 2023. "Information loss in volatility measurement with flat price trading," Empirical Economics, Springer, vol. 64(6), pages 2957-2999, June.
    4. 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.
    5. Bosco, Bruno & Parisio, Lucia & Pelagatti, Matteo & Baldi, Fabio, 2007. "A Robust Multivariate Long Run Analysis of European Electricity Prices," International Energy Markets Working Papers 7438, Fondazione Eni Enrico Mattei (FEEM).
    6. 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.
    7. 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).
    8. Nikolaos Kourogenis, 2015. "Polynomial Trends, Nonstationary Volatility and the Eicker-White Asymptotic Variance Estimator," Economics Bulletin, AccessEcon, vol. 35(3), pages 1675-1680.
    9. Brandan K. Beare, 2008. "Unit Root Testing with Unstable Volatility," Economics Series Working Papers 2008-WO6, University of Oxford, Department of Economics.
    10. Vassilis Polimenis & Ioannis Neokosmidis, 2019. "Non-stationary dividend-price ratios," Journal of Asset Management, Palgrave Macmillan, vol. 20(7), pages 552-567, December.
    11. 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.
    12. 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.
    13. Tao, Yubo, 2019. "Limit theory for moderate deviation from Integrated GARCH processes," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 126-136.
    14. 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.
    15. Skrobotov, Anton, 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.
    16. 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.
    17. Brendan K. Beare, 2018. "Unit Root Testing with Unstable Volatility," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 816-835, November.
    18. 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.
    19. 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.
    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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