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

Author

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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.

Suggested Citation

  • 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.
    • Handle: RePEc:not:notgts:06/04
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    Cited by:

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    3. Taipalus, Katja, 2012. "Detecting asset price bubbles with time-series methods," Scientific Monographs, Bank of Finland, number 2012_047.
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    5. Górecki, Tomasz & Horváth, Lajos & Kokoszka, Piotr, 2018. "Change point detection in heteroscedastic time series," Econometrics and Statistics, Elsevier, vol. 7(C), pages 63-88.
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    7. Halunga, Andreea G. & Osborn, Denise R. & Sensier, Marianne, 2009. "Changes in the order of integration of US and UK inflation," Economics Letters, Elsevier, vol. 102(1), pages 30-32, January.
    8. Uwe Hassler & Jan Scheithauer, 2008. "On Critical Values of Tests against a Change in Persistence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(5), pages 705-710, October.
    9. Lajos Horváth & William Pouliot & Shixuan Wang, 2017. "Detecting at-Most-m Changes in Linear Regression Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(4), pages 552-590, July.
    10. Gabriel Zsurkis & JoÃo Nicolau & Paulo M. M. Rodrigues, 2021. "A Re‐Examination of Inflation Persistence Dynamics in OECD Countries: A New Approach," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(4), pages 935-959, August.
    11. Halunga, Andreea G. & Orme, Chris D. & Yamagata, Takashi, 2017. "A heteroskedasticity robust Breusch–Pagan test for Contemporaneous correlation in dynamic panel data models," Journal of Econometrics, Elsevier, vol. 198(2), pages 209-230.
    12. repec:zbw:bofrdp:2012_007 is not listed on IDEAS
    13. Heinen, Florian & Sibbertsen, Philipp & Kruse, Robinson, 2009. "Forecasting long memory time series under a break in persistence," Hannover Economic Papers (HEP) dp-433, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    14. Zaklan, Aleksandar & Abrell, Jan & Neumann, Anne, 2016. "Stationarity changes in long-run energy commodity prices," Energy Economics, Elsevier, vol. 59(C), pages 96-103.
    15. Petrenko, Victoria (Петренко, ВИктория) & Skrobotov, Anton (Скроботов, Антон) & Turuntseva, Maria (Турунцева, Мария), 2016. "Testing of Changes in Persistence and Their Effect on the Forecasting Quality [Тестирование Изменения Инерционности И Влияние На Качество Прогнозов]," Working Papers 542, Russian Presidential Academy of National Economy and Public Administration.
    16. 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.
    17. Ventosa-Santaulária, Daniel & Gómez-Zaldívar, Manuel, 2009. "Broken mean stationarity and the validity of the Dickey-Fuller test: the case of controlled inflation," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 29(1), May.
    18. 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.
    19. Taipalus, Katja, 2012. "Signaling asset price bubbles with time-series methods," Research Discussion Papers 7/2012, Bank of Finland.
    20. 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.
    21. Heinen, Florian & Willert, Juliane, 2011. "Monitoring a change in persistence of a long range dependent time series," Hannover Economic Papers (HEP) dp-479, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.

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