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Range Unit-Root (RUR) Tests: Robust against Nonlinearities, Error Distributions, Structural Breaks and Outliers

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Author Info

  • Felipe Aparicio
  • Alvaro Escribano
  • Ana E. Sipols

Abstract

Since the seminal paper by Dickey and Fuller in 1979, unit-root tests have conditioned the standard approaches to analysing time series with strong serial dependence in mean behaviour, the focus being placed on the detection of eventual unit roots in an autoregressive model fitted to the series. In this paper, we propose a completely different method to test for the type of long-wave patterns observed not only in unit-root time series but also in series following more complex data-generating mechanisms. To this end, our testing device analyses the unit-root persistence exhibited by the data while imposing very few constraints on the generating mechanism. We call our device the range unit-root (RUR) test since it is constructed from the running ranges of the series from which we derive its limit distribution. These nonparametric statistics endow the test with a number of desirable properties, the invariance to monotonic transformations of the series and the robustness to the presence of important parameter shifts. Moreover, the RUR test outperforms the power of standard unit-root tests on near-unit-root stationary time series; it is invariant with respect to the innovations distribution and asymptotically immune to noise. An extension of the RUR test, called the forward-backward range unit-root (FB-RUR) improves the check in the presence of additive outliers. Finally, we illustrate the performances of both range tests and their discrepancies with the Dickey-Fuller unit-root test on exchange rate series. Copyright 2006 The Authors Journal compilation 2006 Blackwell Publishing Ltd.

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Bibliographic Info

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

Volume (Year): 27 (2006)
Issue (Month): 4 (07)
Pages: 545-576

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Handle: RePEc:bla:jtsera:v:27:y:2006:i:4:p:545-576

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Cited by:
  1. Kunst, Robert M., 2014. "A Combined Nonparametric Test for Seasonal Unit Roots," Economics Series 303, Institute for Advanced Studies.
  2. Ihle, Rico & Brümmer, Bernhard & Thompson, Stanley R., 2009. "Spatial market integration in the EU beef and veal sector: policy decoupling and export bans," DARE Discussion Papers 0913, Georg-August University of Göttingen, Department of Agricultural Economics and Rural Development (DARE).
  3. Francesco D'Amuri & Juri Marcucci, 2012. "The predictive power of Google searches in forecasting unemployment," Temi di discussione (Economic working papers) 891, Bank of Italy, Economic Research and International Relations Area.
  4. Dilip M. Nachane, 2011. "Selected Problems in the Analysis of Nonstationary & Nonlinear Time Series," Journal of Quantitative Economics, The Indian Econometric Society, vol. 9(1), pages 1-17.
  5. Ihle, Rico & Brummer, Bernhard & Thompson, Stanley R., 2010. "Auswirkungen Der Fischler-Reform Und Der Blauzungenkrankheit Auf Die Europäischen Kälbermärkte," 50st Annual Conference, Braunschweig, Germany, September 29-October 1, 2010 93953, German Association of Agricultural Economists (GEWISOLA).
  6. Antonio E. Noriega & Manuel Ramos Francia, 2009. "On the dynamics of inflation persistence around the world," Working Papers 2009-02, Banco de México.
  7. Kunst, Robert M., 2009. "A Nonparametric Test for Seasonal Unit Roots," Economics Series 233, Institute for Advanced Studies.
  8. Jurgen Holl & Robert Kunst, 2011. "Unit root in unemployment - new evidence from nonparametric tests," Applied Economics Letters, Taylor & Francis Journals, vol. 18(6), pages 509-512.
  9. Lindback, Morten & Osmundsen, Petter & Øglend, Atle, 2013. "Shale Gas and the Relationship between U.S. Natural Gas, Liquified Petroleum Gases and Oil Market," UiS Working Papers in Economics and Finance 2013/5, University of Stavanger.
  10. Herwartz, Helmut & Siedenburg, Florian, 2009. "A new approach to unit root testing," Economics Working Papers 2009,06, Christian-Albrechts-University of Kiel, Department of Economics.
  11. Alexeev, Vitali & Maynard, Alex, 2012. "Localized level crossing random walk test robust to the presence of structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3322-3344.
  12. Alvaro Escribano & M. Santos & Ana Sipols, 2008. "Testing for cointegration using induced-order statistics," Computational Statistics, Springer, vol. 23(1), pages 131-151, January.

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