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Tests for Volatility Shifts in Garch Against Long-Range Dependence

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  • Taewook Lee
  • Moosup Kim
  • Changryong Baek

Abstract

type="main" xml:id="jtsa12098-abs-0001"> Many empirical findings show that volatility in financial time series exhibits high persistence. Some researchers argue that such persistency is due to volatility shifts in the market, while others believe that this is a natural fluctuation explained by stationary long-range dependence models. These two approaches confuse many practitioners, and forecasts for future volatility are dramatically different depending on which models to use. In this article, therefore, we consider a statistical testing procedure to distinguish volatility shifts in generalized AR conditional heteroscedasticity (GARCH) model against long-range dependence. Our testing procedure is based on the residual-based cumulative sum test, which is designed to correct the size distortion observed for GARCH models. We examine the validity of our method by providing asymptotic distributions of test statistic. Also, Monte Carlo simulations study shows that our proposed method achieves a good size while providing a reasonable power against long-range dependence. It is also observed that our test is robust to the misspecified GARCH models.

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  • Taewook Lee & Moosup Kim & Changryong Baek, 2015. "Tests for Volatility Shifts in Garch Against Long-Range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 127-153, March.
    • Handle: RePEc:bla:jtsera:v:36:y:2015:i:2:p:127-153
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    File URL: http://hdl.handle.net/10.1111/jtsa.12098
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    1. Giot, Pierre & Laurent, Sebastien, 2004. "Modelling daily Value-at-Risk using realized volatility and ARCH type models," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 379-398, June.
    2. Elena Andreou & Eric Ghysels, 2002. "Detecting multiple breaks in financial market volatility dynamics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 579-600.
    3. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
    4. Bai, Jushan, 1997. "Estimating Multiple Breaks One at a Time," Econometric Theory, Cambridge University Press, vol. 13(3), pages 315-352, June.
    5. Changryong Baek & Vladas Pipiras, 2012. "Statistical tests for a single change in mean against long‐range dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(1), pages 131-151, January.
    6. Giraitis, Liudas & Robinson, Peter & Surgailis, Donatas, 2000. "A model for long memory conditional heteroscedasticity," LSE Research Online Documents on Economics 2103, London School of Economics and Political Science, LSE Library.
    7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    8. Hartz, Christoph & Mittnik, Stefan & Paolella, Marc, 2006. "Accurate value-at-risk forecasting based on the normal-GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2295-2312, December.
    9. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    10. Giraitis, Liudas & Robinson, Peter M. & Surgailis, Donatas, 2000. "A model for long memory conditional heteroscedasticity," LSE Research Online Documents on Economics 299, London School of Economics and Political Science, LSE Library.
    11. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July.
    12. Robinson, P. M., 2001. "The memory of stochastic volatility models," Journal of Econometrics, Elsevier, vol. 101(2), pages 195-218, April.
    13. Jensen Anders Tolver & Lange Theis, 2010. "On Convergence of the QMLE for Misspecified GARCH Models," Journal of Time Series Econometrics, De Gruyter, vol. 2(1), pages 1-31, June.
    14. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    15. Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 2002. "Regular variation of GARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 95-115, May.
    16. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    17. Koichi Maekawa & Sangyeol & Lee, 2004. "The Cusum Test for Parameter Change in Regression with ARCH Errors," Econometric Society 2004 Far Eastern Meetings 606, Econometric Society.
    18. Thomas Mikosch & Cătălin Stărică, 2004. "Nonstationarities in Financial Time Series, the Long-Range Dependence, and the IGARCH Effects," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 378-390, February.
    19. de Pooter, M.D. & van Dijk, D.J.C., 2004. "Testing for changes in volatility in heteroskedastic time series - a further examination," Econometric Institute Research Papers EI 2004-38, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    20. Peter M Robinson, 2001. "The Memory of Stochastic Volatility Models," STICERD - Econometrics Paper Series 410, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    21. Hillebrand, Eric, 2005. "Neglecting parameter changes in GARCH models," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 121-138.
    22. Francq, Christian & Zakoian, Jean-Michel, 2007. "Quasi-maximum likelihood estimation in GARCH processes when some coefficients are equal to zero," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1265-1284, September.
    23. Robinson, Peter M., 2001. "The memory of stochastic volatility models," LSE Research Online Documents on Economics 2298, London School of Economics and Political Science, LSE Library.
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    Cited by:

    1. Byungsoo Kim & Junmo Song & Changryong Baek, 2021. "Robust test for structural instability in dynamic factor models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(4), pages 821-853, August.
    2. Lee, Taewook & Baek, Changryong, 2020. "Block wild bootstrap-based CUSUM tests robust to high persistence and misspecification," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    3. Song, Junmo & Baek, Changryong, 2019. "Detecting structural breaks in realized volatility," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 58-75.

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