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Recent developments in bootstrap methods for dependent data

Author

Listed:
  • Giuseppe Cavaliere
  • Dimitris N. Politis
  • Anders Rahbek
  • Giuseppe Cavaliere
  • Anders Rahbek
  • A. M. Robert Taylor

Abstract

type="main" xml:id="jtsa12104-abs-0001"> In a recent paper, Cavaliere et al., develop bootstrap implementations of the popular likelihood-based co-integration rank tests and associated sequential rank determination procedures of Johansen . By using estimates of the parameters of the underlying co-integrated VAR model obtained under the restriction of the null hypothesis, they show that consistent bootstrap inference can be obtained for processes whose deterministic component is either zero, a restricted constant or a restricted trend. In this article, we extend their bootstrap approach to allow the deterministic component to follow the practically relevant cases of either an unrestricted constant or an unrestricted trend from Johansen . A full asymptotic theory is provided for these two cases, establishing the asymptotic validity of the resulting bootstrap tests. Our results, taken together with those in Cavaliere et al., , therefore show that the bootstrap approach based on imposing the reduced rank null hypothesis is valid for all five of these deterministic settings. Monte Carlo evidence demonstrates the improvements that the proposed bootstrap methods can deliver over the corresponding asymptotic procedures.

Suggested Citation

  • Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Giuseppe Cavaliere & Anders Rahbek & A. M. Robert Taylor, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 272-289, May.
    • Handle: RePEc:bla:jtsera:v:36:y:2015:i:3:p:272-289
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    1. Anders Rygh Swensen, 2006. "Bootstrap Algorithms for Testing and Determining the Cointegration Rank in VAR Models -super-1," Econometrica, Econometric Society, vol. 74(6), pages 1699-1714, November.
    2. Giuseppe Cavaliere & A. M. Robert Taylor & Carsten Trenkler, 2013. "Bootstrap Cointegration Rank Testing: The Role of Deterministic Variables and Initial Values in the Bootstrap Recursion," Econometric Reviews, Taylor & Francis Journals, vol. 32(7), pages 814-847, October.
    3. Giuseppe Cavaliere & Anders Rahbek & A. M. Robert Taylor, 2014. "Bootstrap Determination of the Co-Integration Rank in Heteroskedastic VAR Models," Econometric Reviews, Taylor & Francis Journals, vol. 33(5-6), pages 606-650, August.
    4. Shao, Xiaofeng, 2010. "The Dependent Wild Bootstrap," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 218-235.
    5. Bent Nielsen & Anders Rahbek, 2000. "Similarity Issues in Cointegration Analysis," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 62(1), pages 5-22, February.
    6. Paul Turner, 2009. "Testing for cointegration using the Johansen approach: are we using the correct critical values?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(5), pages 825-831.
    7. Aznar, Antonio & Salvador, Manuel, 2002. "Selecting The Rank Of The Cointegration Space And The Form Of The Intercept Using An Information Criterion," Econometric Theory, Cambridge University Press, vol. 18(4), pages 926-947, August.
    8. Paruolo Paolo, 2005. "Design of vector autoregressive processes for invariant statistics," Economics and Quantitative Methods qf0504, Department of Economics, University of Insubria.
    9. Johansen, Soren, 1992. "Determination of Cointegration Rank in the Presence of a Linear Trend," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 383-397, August.
    10. Soren Johansen, 2002. "A Small Sample Correction for the Test of Cointegrating Rank in the Vector Autoregressive Model," Econometrica, Econometric Society, vol. 70(5), pages 1929-1961, September.
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    1. Germán Aneiros & Paula Raña & Philippe Vieu & Juan Vilar, 2018. "Bootstrap in semi-functional partial linear regression under dependence," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 659-679, September.

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