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

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  • Felipe Aparicio
  • Alvaro Escribano
  • Ana E. Sipols

Abstract

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.

Suggested Citation

  • Felipe Aparicio & Alvaro Escribano & Ana E. Sipols, 2006. "Range Unit‐Root (RUR) Tests: Robust against Nonlinearities, Error Distributions, Structural Breaks and Outliers," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(4), pages 545-576, July.
  • Handle: RePEc:bla:jtsera:v:27:y:2006:i:4:p:545-576
    DOI: 10.1111/j.1467-9892.2006.00474.x
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    File URL: https://doi.org/10.1111/j.1467-9892.2006.00474.x
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    1. Pierre Perron & Gabriel RodrÌguez, 2003. "Searching For Additive Outliers In Nonstationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(2), pages 193-220, March.
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    Cited by:

    1. Dean Fantazzini, 2014. "Nowcasting and Forecasting the Monthly Food Stamps Data in the US Using Online Search Data," PLOS ONE, Public Library of Science, vol. 9(11), pages 1-27, November.
    2. Atle Oglend, Morten E. Lindbäck, and Petter Osmundsen, 2015. "Shale Gas Boom Affecting the Relationship Between LPG and Oil Prices," The Energy Journal, International Association for Energy Economics, vol. 0(Number 4).
    3. Bruno Larue & Jean-Philippe Gervais & Yannick Rancourt, 2010. "Exchange rate pass-through, menu costs and threshold cointegration," Empirical Economics, Springer, vol. 38(1), pages 171-192, February.
    4. D’Amuri, Francesco & Marcucci, Juri, 2017. "The predictive power of Google searches in forecasting US unemployment," International Journal of Forecasting, Elsevier, vol. 33(4), pages 801-816.
    5. 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.
    6. V. A. Reisen & C. Lévy-Leduc & M. Bourguignon & H. Boistard, 2017. "Robust Dickey–Fuller tests based on ranks for time series with additive outliers," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(1), pages 115-131, January.
    7. Fantazzini, Dean & Toktamysova, Zhamal, 2015. "Forecasting German car sales using Google data and multivariate models," International Journal of Production Economics, Elsevier, vol. 170(PA), pages 97-135.
    8. Tamer Kulaksizoglu, 2016. "Measuring the Turkish core inflation with a shifting mean model," Empirical Economics, Springer, vol. 51(1), pages 57-70, August.
    9. 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.
    10. 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.
    11. 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).
    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.
    13. Ihle, Rico & Brümmer, Bernhard & Thompson, Stanley R., 2010. "Auswirkungen Der Fischler-Reform Und Der Blauzungenkrankheit Auf Die Europäischen Kälbermärkte," 50th Annual Conference, Braunschweig, Germany, September 29-October 1, 2010 93953, German Association of Agricultural Economists (GEWISOLA).
    14. Helmut Herwartz & Florian Siedenburg, 2010. "A New Approach to Unit Root Testing," Computational Economics, Springer;Society for Computational Economics, vol. 36(4), pages 365-384, December.
    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. Kunst, Robert M., 2014. "A Combined Nonparametric Test for Seasonal Unit Roots," Economics Series 303, Institute for Advanced Studies.
    17. Kunst, Robert M., 2009. "A Nonparametric Test for Seasonal Unit Roots," Economics Series 233, Institute for Advanced Studies.
    18. 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.
    19. 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.

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