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Testing for a break in persistence under long-range dependencies

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  • Philipp Sibbertsen
  • Robinson Kruse

Abstract

We show that tests for a break in the persistence of a time series in the classical I(0)/I(1) framework have serious size distortions when the actual data-generating process (DGP) exhibits long-range dependencies. We prove that the limiting distribution of a CUSUM of squares-based test depends on the true memory parameter if the DGP exhibits long memory. We propose adjusted critical values for the test and give finite sample response curves that allow easy implementation of the test by the practitioner and also ease in computing the relevant critical values. We furthermore prove the consistency of the test for a simple breakpoint estimator also under long memory. We show that the test has satisfying power properties when the correct critical values are used. Copyright 2009 The Authors. Journal compilation 2009 Blackwell Publishing Ltd

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Bibliographic Info

Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

Volume (Year): 30 (2009)
Issue (Month): 3 (05)
Pages: 263-285

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Handle: RePEc:bla:jtsera:v:30:y:2009:i:3:p:263-285

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  1. Gerard O'Reilly & Karl Whelan, 2005. "Has Euro-Area Inflation Persistence Changed Over Time?," The Review of Economics and Statistics, MIT Press, vol. 87(4), pages 709-720, November.
  2. Kim, Jae-Young, 2000. "Detection of change in persistence of a linear time series," Journal of Econometrics, Elsevier, Elsevier, vol. 95(1), pages 97-116, March.
  3. Pivetta, Frederic & Reis, Ricardo, 2007. "The persistence of inflation in the United States," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 31(4), pages 1326-1358, April.
  4. 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, American Statistical Association, vol. 10(3), pages 271-87, July.
  5. Lanne , Markku, 2002. "Nonlinear dynamics of interest rate and inflation," Research Discussion Papers, Bank of Finland 21/2002, Bank of Finland.
  6. 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, Elsevier, vol. 109(2), pages 389-392, August.
  7. 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, Wiley Blackwell, vol. 28(3), pages 408-433, 05.
  8. Hassler, Uwe & Wolters, Jurgen, 1995. "Long Memory in Inflation Rates: International Evidence," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 13(1), pages 37-45, January.
  9. Busetti, Fabio & Taylor, A. M. Robert, 2004. "Tests of stationarity against a change in persistence," Journal of Econometrics, Elsevier, Elsevier, vol. 123(1), pages 33-66, November.
  10. 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, Royal Economic Society, vol. 6(2), pages 291-311, December.
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