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Testing for a change in persistence in the presence of non-stationary volatility

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  • Cavaliere, Giuseppe
  • Taylor, A.M. Robert

Abstract

In this paper we consider tests for the null of (trend-) stationarity against the alternative of a change in persistence at some (known or unknown) point in the observed sample, either from I(0) to I(1) behaviour or vice versa, of, inter alia, [Kim, J., 2000. Detection of change in persistence of a linear time series. Journal of Econometrics 95, 97-116]. We show that in circumstances where the innovation process displays non-stationary unconditional volatility of a very general form, which includes single and multiple volatility breaks as special cases, the ratio-based statistics used to test for persistence change do not have pivotal limiting null distributions. Numerical evidence suggests that this can cause severe over-sizing in the tests. In practice it may therefore be hard to discriminate between persistence change processes and processes with constant persistence but which display time-varying unconditional volatility. We solve the identified inference problem by proposing wild bootstrap-based implementations of the tests. Monte Carlo evidence suggests that the bootstrap tests perform well in finite samples. An empirical illustration using USÂ price inflation data is provided.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 147 (2008)
Issue (Month): 1 (November)
Pages: 84-98
Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Handle: RePEc:eee:econom:v:147:y:2008:i:1:p:84-98

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Web page: http://www.elsevier.com/locate/jeconom

For corrections or technical questions regarding this item, or to correct its listing, contact: (Jeroen Loos).

Related research

Keywords: Persistence change Non-stationary volatility Wild bootstrap;

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References

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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. Leybourne, Stephen & Taylor, A. M. Robert, 2004. "On tests for changes in persistence," Economics Letters, Elsevier, vol. 84(1), pages 107-115, July.
  2. Anindya Banerjee & Robin L. Lumsdaine & James H. Stock, 1990. "Recursive and Sequential Tests of the Unit Root and Trend Break Hypothesis: Theory and International Evidence," NBER Working Papers 3510, National Bureau of Economic Research, Inc.
  3. M Sensier & D van Dijk, 2003. "Testing for Volatility Changes in US Macroeconomic Time Series," Centre for Growth and Business Cycle Research Discussion Paper Series 36, Economics, The Univeristy of Manchester.
  4. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-30, March.
  5. Margaret M. McConnell & Gabriel Perez-Quiros, 2000. "Output Fluctuations in the United States: What Has Changed since the Early 1980's?," American Economic Review, American Economic Association, vol. 90(5), pages 1464-1476, December.
  6. Giuseppe Cavaliere, 2005. "Unit Root Tests under Time-Varying Variances," Econometric Reviews, Taylor and Francis Journals, vol. 23(3), pages 259-292.
  7. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
  8. Phillips, Peter C B & Xiao, Zhijie, 1998. " A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-69, December.
  9. Emmanuel Flachaire, 2001. "The Wild Bootstrap, Tamed at Last," STICERD - Distributional Analysis Research Programme Papers 58, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  10. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
  11. Kim, Tae-Hwan & Leybourne, Stephen & Newbold, Paul, 2002. "Unit root tests with a break in innovation variance," Journal of Econometrics, Elsevier, vol. 109(2), pages 365-387, August.
  12. Cavaliere, Giuseppe, 2004. "Testing stationarity under a permanent variance shift," Economics Letters, Elsevier, vol. 82(3), pages 403-408, March.
  13. Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation for Research in Economics, Yale University.
  14. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2007. "Testing for unit roots in time series models with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 140(2), pages 919-947, October.
  15. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
  16. 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.
  17. 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.
  18. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
  19. repec:cup:etheor:v:24:y:2007:i:01:p:72-87_08 is not listed on IDEAS
  20. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  21. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2005. "Stationarity Tests Under Time-Varying Second Moments," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1112-1129, December.
  22. Fabio Busetti & Andrew C Harvey, 1998. "Testing for the Presence of a Random Walk in Series with Structural Breaks - (Now published in Journal of Time Series Analysis, 22 (2001), pp.127-150.)," STICERD - Econometrics Paper Series /1998/365, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  23. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  24. Hansen, Bruce E, 1995. "Regression with Nonstationary Volatility," Econometrica, Econometric Society, vol. 63(5), pages 1113-32, September.
  25. 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.
  26. Busetti, Fabio & Taylor, A M Robert, 2003. "Variance Shifts, Structural Breaks, and Stationarity Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 510-31, October.
  27. 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.
  28. de Jong, Robert M., 2000. "A Strong Consistency Proof For Heteroskedasticity And Autocorrelation Consistent Covariance Matrix Estimators," Econometric Theory, Cambridge University Press, vol. 16(02), pages 262-268, April.
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Citations

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Cited by:
  1. Heinen, Florian & Sibbertsen, Philipp & Kruse, Robinson, 2009. "Forecasting long memory time series under a break in persistence," Diskussionspapiere der Wirtschaftswissenschaftlichen Fakultät der Universität Hannover dp-433, Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  2. Andreea Halunga & Chris D. Orme & Takashi Yamagata, 2011. "A Heteroskedasticity Robust Breusch-Pagan Test for Contemporaneous Correlation in Dynamic Panel Data Models," The School of Economics Discussion Paper Series 1118, Economics, The University of Manchester.
  3. Heinen, Florian & Willert, Juliane, 2011. "Monitoring a change in persistence of a long range dependent time series," Diskussionspapiere der Wirtschaftswissenschaftlichen Fakultät der Universität Hannover dp-479, Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  4. Aleksandar Zaklan & Jan Abrell & Anne Neumann, 2011. "Stationarity Changes in Long-Run Fossil Resource Prices: Evidence from Persistence Break Testing," Discussion Papers of DIW Berlin 1152, DIW Berlin, German Institute for Economic Research.

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