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Testing for a break in persistence under long-range dependencies and mean shifts

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  • Philipp Sibbertsen

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  • Juliane Willert

Abstract

We show that the CUSUM-squared based test for a change in persistence by Leybourne et al. (2007) is not robust against shifts in the mean. A mean shift leads to serious size distortions. Therefore, adjusted critical values are needed when it is known that the data generating process has a mean shift. These are given for the case of one mean break. Response curves for the critical values are derived and a Monte Carlo study showing the size and power properties under this general de-trending is given
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Suggested Citation

  • Philipp Sibbertsen & Juliane Willert, 2012. "Testing for a break in persistence under long-range dependencies and mean shifts," Statistical Papers, Springer, vol. 53(2), pages 357-370, May.
  • Handle: RePEc:spr:stpapr:v:53:y:2012:i:2:p:357-370
    DOI: 10.1007/s00362-010-0342-5
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    References listed on IDEAS

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    1. Philipp Sibbertsen, 2004. "Long memory versus structural breaks: An overview," Statistical Papers, Springer, vol. 45(4), pages 465-515, October.
    2. 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, May.
    3. Philipp Sibbertsen & Juliane Willert, 2012. "Testing for a break in persistence under long-range dependencies and mean shifts," Statistical Papers, Springer, vol. 53(2), pages 357-370, May.
    4. 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, May.
    5. Banerjee, Anindya & Lumsdaine, Robin L & Stock, James H, 1992. "Recursive and Sequential Tests of the Unit-Root and Trend-Break Hypotheses: Theory and International Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 271-287, July.
    6. Belaire-Franch, Jorge, 2005. "A Proof Of The Power Of Kim'S Test Against Stationary Processes With Structural Breaks," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1172-1176, December.
    7. 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.
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    Citations

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    Cited by:

    1. Nguyen, Duc Binh Benno & Prokopczuk, Marcel & Sibbertsen, Philipp, 2017. "The Memory of Stock Return Volatility: Asset Pricing Implications," Hannover Economic Papers (HEP) dp-613, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    2. Michael Frömmel & Robinson Kruse, 2012. "Testing for a rational bubble under long memory," Quantitative Finance, Taylor & Francis Journals, vol. 12(11), pages 1723-1732, November.
    3. Kruse, Robinson & Sibbertsen, Philipp, 2012. "Long memory and changing persistence," Economics Letters, Elsevier, vol. 114(3), pages 268-272.
    4. Philipp Sibbertsen & Juliane Willert, 2012. "Testing for a break in persistence under long-range dependencies and mean shifts," Statistical Papers, Springer, vol. 53(2), pages 357-370, May.
    5. repec:eme:jespps:jes-10-2015-0190 is not listed on IDEAS
    6. repec:eee:intfin:v:50:y:2017:i:c:p:36-51 is not listed on IDEAS
    7. Davide Delle Monache & Stefano Grassi & Paolo Santucci de Magistris, 0404. "Does the ARFIMA really shift?," CREATES Research Papers 2017-16, Department of Economics and Business Economics, Aarhus University.
    8. Hassler, Uwe & Rodrigues, Paulo M.M. & Rubia, Antonio, 2014. "Persistence in the banking industry: Fractional integration and breaks in memory," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 95-112.
    9. Erhard Reschenhofer & Werner Ploberger & Georg Lehecka, 2014. "Detecting fuzzy periodic patterns in futures spreads," Statistical Papers, Springer, vol. 55(2), pages 487-496, May.
    10. Giorgio Canarella & Stephen Miller, 2016. "Inflation persistence and structural breaks: the experience of inflation targeting countries and the US," Journal of Economic Studies, Emerald Group Publishing, vol. 43(6), pages 980-1005, November.
    11. 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.
    12. Juan Carlos Cuestas & Luis A. Gil-Alana & Paulo José Regis, 2015. "The Sustainability of European External Debt: What have We Learned?," Review of International Economics, Wiley Blackwell, vol. 23(3), pages 445-468, August.
    13. Frömmel, Michael & Kruse, Robinson, 2015. "Interest rate convergence in the EMS prior to European Monetary Union," Journal of Policy Modeling, Elsevier, vol. 37(6), pages 990-1004.
    14. repec:spr:empeco:v:54:y:2018:i:4:d:10.1007_s00181-017-1276-8 is not listed on IDEAS
    15. Katarzyna Łasak & Carlos Velasco, 2015. "Fractional Cointegration Rank Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 241-254, April.
    16. Guglielmo Caporale & Luis Gil-Alana, 2013. "Long memory in US real output per capita," Empirical Economics, Springer, vol. 44(2), pages 591-611, April.
    17. repec:spr:stpapr:v:58:y:2017:i:3:d:10.1007_s00362-015-0722-y is not listed on IDEAS
    18. Chen, Zhanshou & Xing, Yuhong & Li, Fuxiao, 2016. "Sieve bootstrap monitoring for change from short to long memory," Economics Letters, Elsevier, vol. 140(C), pages 53-56.
    19. Sibbertsen, Philipp & Wegener, Christoph & Basse, Tobias, 2014. "Testing for a break in the persistence in yield spreads of EMU government bonds," Journal of Banking & Finance, Elsevier, vol. 41(C), pages 109-118.
    20. repec:eee:jebusi:v:92:y:2017:i:c:p:45-62 is not listed on IDEAS

    More about this item

    Keywords

    Break in persistence; Long memory; Structural break; Level shift; C12; C22;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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