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

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  • Giuseppe Cavaliere
  • A. M. Robert Taylor

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 (2000). 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 application to a variety of measures of U.S. price inflation data is provided.

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Bibliographic Info

Paper provided by University of Nottingham, Granger Centre for Time Series Econometrics in its series Discussion Papers with number 06/04.

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Date of creation: Jul 2006
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Handle: RePEc:not:notgts:06/04

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Postal: School of Economics University of Nottingham University Park Nottingham NG7 2RD
Phone: (44) 0115 951 5620
Fax: (0115) 951 4159
Web page: http://www.nottingham.ac.uk/economics/grangercentre/
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Related research

Keywords: Persistence change; non-stationary volatility; wild bootstrap;

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References

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  1. 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.
  2. 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.
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  4. 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.
  5. Russell Davidson & Emmanuel Flachaire, 2001. "The wild bootstrap, tamed at last," LSE Research Online Documents on Economics 6560, London School of Economics and Political Science, LSE Library.
  6. Hansen, Bruce E, 1995. "Regression with Nonstationary Volatility," Econometrica, Econometric Society, vol. 63(5), pages 1113-32, September.
  7. 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.
  8. Giuseppe Cavaliere, 2003. "Unit root tests under time-varying variances," Quaderni di Dipartimento 2, Department of Statistics, University of Bologna.
  9. Margaret McConnell & Gabriel Perez Quiros, 2000. "Output fluctuations in the United States: what has changed since the early 1980s?," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
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  11. Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "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?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale University.
  12. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2008. "Testing for a change in persistence in the presence of non-stationary volatility," Journal of Econometrics, Elsevier, vol. 147(1), pages 84-98, November.
  13. Marianne Sensier & Dick van Dijk, 2004. "Testing for Volatility Changes in U.S. Macroeconomic Time Series," The Review of Economics and Statistics, MIT Press, vol. 86(3), pages 833-839, August.
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  19. 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.
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Citations

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Cited by:
  1. 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.
  2. Taipalus, Katja, 2012. "Detecting asset price bubbles with time-series methods," Scientific Monographs E:47/2012, Bank of Finland.
  3. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2008. "Testing for a change in persistence in the presence of non-stationary volatility," Journal of Econometrics, Elsevier, vol. 147(1), pages 84-98, November.
  4. Heinen, Florian & Willert, Juliane, 2011. "Monitoring a change in persistence of a long range dependent time series," Diskussionspapiere der Wirtschaftswissenschaftlichen Fakultät der Leibniz Universität Hannover dp-479, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  5. 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.
  6. Chen, Zhanshou & Tian, Zheng & Wei, Yuesong, 2010. "Monitoring change in persistence in linear time series," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1520-1527, October.
  7. 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.
  8. Chen, Zhanshou & Jin, Zi & Tian, Zheng & Qi, Peiyan, 2012. "Bootstrap testing multiple changes in persistence for a heavy-tailed sequence," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2303-2316.
  9. Taipalus , Katja, 2012. "Signaling asset price bubbles with time-series methods," Research Discussion Papers 7/2012, Bank of Finland.

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