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Monitoring a change in persistence of a long range dependent time series

  • Heinen, Florian
  • Willert, Juliane

We consider the detection of a change in persistence of a long range dependent time series. The usual approach is to use one-shot tests to detect a change in persistence a posteriori in a historical data set. However, as breaks can occur at any given time and data arrives steadily it is desirable to detect a change in persistence as soon as possible. We propose the use of a MOSUM type test which allows sequential application whenever new data arrives. We derive the asymptotic distribution of the test statistic and prove consistency. We further study the finite sample behavior of the test and provide an empirical application.

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Paper provided by Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät in its series Hannover Economic Papers (HEP) with number dp-479.

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Length: 21 pages
Date of creation: Sep 2011
Date of revision:
Handle: RePEc:han:dpaper:dp-479
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  1. Leisch, Friedrich & Hornik, Kurt & Kuan, Chung-Ming, 2000. "Monitoring Structural Changes With The Generalized Fluctuation Test," Econometric Theory, Cambridge University Press, vol. 16(06), pages 835-854, December.
  2. Busetti, Fabio & Taylor, A. M. Robert, 2004. "Tests of stationarity against a change in persistence," Journal of Econometrics, Elsevier, vol. 123(1), pages 33-66, November.
  3. Filippo Altissimo & Valentina Corradi, 2000. "Strong Rules for Detecting the Number of Breaks in a Time Series," Econometric Society World Congress 2000 Contributed Papers 0574, Econometric Society.
  4. Altissimo, Filippo & Corradi, Valentina, 2003. "Strong rules for detecting the number of breaks in a time series," Journal of Econometrics, Elsevier, vol. 117(2), pages 207-244, December.
  5. Stephen Leybourne & Tae-Hwan Kim & Vanessa Smith & Paul Newbold, 2003. "Tests for a change in persistence against the null of difference-stationarity," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 291-311, December.
  6. Fulvio Corsi & Stefan Mittnik & Christian Pigorsch & Uta Pigorsch, 2008. "The Volatility of Realized Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 46-78.
  7. Florian Heinen & Philipp Sibbertsen & Robinson Kruse, 2009. "Forecasting long memory time series under a break in persistence," CREATES Research Papers 2009-53, School of Economics and Management, University of Aarhus.
  8. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
  9. Chu, Chia-Shang James & Stinchcombe, Maxwell & White, Halbert, 1996. "Monitoring Structural Change," Econometrica, Econometric Society, vol. 64(5), pages 1045-65, September.
  10. Hassler, Uwe & Wolters, Jurgen, 1995. "Long Memory in Inflation Rates: International Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 37-45, January.
  11. Kurt Hornik & Friedrich Leisch & Christian Kleiber & Achim Zeileis, 2005. "Monitoring structural change in dynamic econometric models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(1), pages 99-121.
  12. Allan Timmermann & M. Hashem Pesaran, 2003. "Small Sample Properties of Forecasts from Autoregressive Models under Structural Breaks," CESifo Working Paper Series 990, CESifo Group Munich.
  13. Kim, Jae-Young, 2000. "Detection of change in persistence of a linear time series," Journal of Econometrics, Elsevier, vol. 95(1), pages 97-116, March.
  14. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
  15. de Jong, Robert M. & Davidson, James, 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I," Econometric Theory, Cambridge University Press, vol. 16(05), pages 621-642, October.
  16. Ghysels, E. & Guay, A. & Hall, A., 1995. "Predictive Tests for Structural Change with Unknown Breakpoint," Cahiers de recherche 9524, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  17. Philipp Sibbertsen & Robinson Kruse, 2009. "Testing for a break in persistence under long-range dependencies," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(3), pages 263-285, 05.
  18. James H. Stock & Mark W. Watson, 2005. "Implications of Dynamic Factor Models for VAR Analysis," NBER Working Papers 11467, National Bureau of Economic Research, Inc.
  19. Stephen Leybourne & Robert Taylor & Tae-Hwan Kim, 2007. "CUSUM of Squares-Based Tests for a Change in Persistence," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(3), pages 408-433, 05.
  20. Hassler, Uwe & Nautz, Dieter, 2008. "On the persistence of the Eonia spread," Economics Letters, Elsevier, vol. 101(3), pages 184-187, December.
  21. Giuseppe Cavaliere & A. M. Robert Taylor, 2006. "Testing for a change in persistence in the presence of non-stationary volatility," Discussion Papers 06/04, University of Nottingham, Granger Centre for Time Series Econometrics.
  22. Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March.
  23. Chu, C.S.J. & Hornik, K. & Kuan, C.M., 1993. "Mosum Tests for Parameter Constancy," Papers 9319, Southern California - Department of Economics.
  24. Kim, Jae-Young & Belaire-Franch, Jorge & Amador, Rosa Badillo, 2002. "Corrigendum to "Detection of change in persistence of a linear time series" [J. Econom. 95 (2000) 97-116]," Journal of Econometrics, Elsevier, vol. 109(2), pages 389-392, August.
  25. Andreou, Elena & Ghysels, Eric, 2006. "Monitoring disruptions in financial markets," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 77-124.
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