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CUSUM of Squares-Based Tests for a Change in Persistence

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  • Stephen Leybourne
  • Robert Taylor
  • Tae-Hwan Kim

Abstract

Using standardized cumulative sums of squared sub-sample residuals, we propose a new ratio-based test of the null hypothesis that a time series exhibits no change in its persistence structure [specifically that it displays constant I(1) behaviour] against the alternative of a change in persistence from trend stationarity to difference stationarity, or vice versa. Neither the direction nor location of any possible change under the alternative hypothesis need be assumed known. A key feature of our proposed test which distinguishes it from extant tests for persistence change [certain of which test the null hypothesis of constant I(0) behaviour while others, like our proposed test, test the null hypothesis of constant I(1) behaviour] is that it displays no tendency to spuriously over-reject when applied to series which, although not constant I(1) series, do not display a change in persistence [specifically are constant I(0) processes]. Moreover, where our ratio test correctly rejects the null of no persistence change, the tail in which the rejection occurs can also be used to identify the direction of change since, even in relatively small samples, the test almost never rejects in the right [left] tail when there is a change from I(0) to I(1) [I(1) to I(0)]. Again this useful property is not shared by existing tests. As a by-product of our analysis, we also propose breakpoint estimators which are consistent where the timing of the change in persistence is unknown. Copyright 2007 The Authors Journal compilation 2007 Blackwell Publishing Ltd.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:jtsera:v:28:y:2007:i:3:p:408-433
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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. 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.
    4. 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.
    5. Chen, Wei & Huang, Zhuo & Yi, Yanping, 2015. "Is there a structural change in the persistence of WTI–Brent oil price spreads in the post-2010 period?," Economic Modelling, Elsevier, vol. 50(C), pages 64-71.
    6. Florian Heinen & Philipp Sibbertsen & Robinson Kruse, 2009. "Forecasting long memory time series under a break in persistence," CREATES Research Papers 2009-53, Department of Economics and Business Economics, Aarhus University.
    7. Uwe Hassler & Jan Scheithauer, 2011. "Detecting changes from short to long memory," Statistical Papers, Springer, vol. 52(4), pages 847-870, November.
    8. Robinson Kruse, "undated". "Forecasting autoregressive time series under changing persistenceCreation-Date: 20100701," CREATES Research Papers 2010-28, Department of Economics and Business Economics, Aarhus University.
    9. Kruse Robinson & Ventosa-Santaulària Daniel & Noriega Antonio E., 2017. "Changes in persistence, spurious regressions and the Fisher hypothesis," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(3), pages 1-28, June.
    10. Kruse, Robinson & Sibbertsen, Philipp, 2012. "Long memory and changing persistence," Economics Letters, Elsevier, vol. 114(3), pages 268-272.
    11. Kruse, Robinson, 2011. "On European monetary integration and the persistence of real effective exchange rates," Finance Research Letters, Elsevier, vol. 8(1), pages 45-50, March.
    12. Martins, Luis F. & Rodrigues, Paulo M.M., 2014. "Testing for persistence change in fractionally integrated models: An application to world inflation rates," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 502-522.
    13. Hirsch, Tristan & Rinke, Saskia, 2017. "Changes in Persistence in Outlier Contaminated Time Series," Hannover Economic Papers (HEP) dp-583, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    14. 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.
    15. Antonio Noriega & Carlos Capistrán & Manuel Ramos-Francia, 2013. "On the dynamics of inflation persistence around the world," Empirical Economics, Springer, vol. 44(3), pages 1243-1265, June.
    16. Nuno Sobreira & Luis C. Nunes, 2016. "Tests for Multiple Breaks in the Trend with Stationary or Integrated Shocks," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 78(3), pages 394-411, June.
    17. repec:eee:intfin:v:50:y:2017:i:c:p:36-51 is not listed on IDEAS
    18. Kruse, Yves Robinson & Kaufmann, Hendrik, 2015. "Bias-corrected estimation in mildly explosive autoregressions," Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112897, Verein für Socialpolitik / German Economic Association.
    19. Noriega Antonio E. & Ramos Francia Manuel, 2008. "A Note on the Dynamics of Persistence in US Inflation," Working Papers 2008-12, Banco de México.
    20. 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.
    21. 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.
    22. Simeon Coleman Author name: Vitor Leone, 2012. "Time-series characteristics of UK commercial property returns: Testing for multiple changes in persistence," Working Papers 2012/03, Nottingham Trent University, Nottingham Business School, Economics Division.
    23. Hendrik Kaufmannz & Robinson Kruse, 2013. "Bias-corrected estimation in potentially mildly explosive autoregressive models," CREATES Research Papers 2013-10, Department of Economics and Business Economics, Aarhus University.
    24. 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.
    25. 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.

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