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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

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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  • 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
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    References listed on IDEAS

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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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    1. 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.
    2. Ihle, Rico & Brümmer, 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).
    3. Alvaro Escribano & M. Santos & Ana Sipols, 2008. "Testing for cointegration using induced-order statistics," Computational Statistics, Springer, vol. 23(1), pages 131-151, January.
    4. 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).
    5. Tamer Kulaksizoglu, 2016. "Measuring the Turkish core inflation with a shifting mean model," Empirical Economics, Springer, vol. 51(1), pages 57-70, August.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Ihle, Rico & Brümmer, Bernhard & Thompson, Stanley R., 2009. "Spatial Market Integration in the EU Beef and Veal Sector: Policy Decoupling and Export Bans," 54th Annual Conference, Goettingen, Germany, September 17-19, 2014 187443, German Association of Agricultural Economists (GEWISOLA).
    14. Fantazziini, Dean, 2014. "Nowcasting and Forecasting the Monthly Food Stamps Data in the US using Online Search Data," MPRA Paper 59696, University Library of Munich, Germany.
    15. 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.
    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.

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