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Testing joint hypotheses when one of the alternatives is one-sided

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  • K Abadir
  • W Distaso

Abstract

We propose a class of statistics where the direction of one of the alternatives is incorporated. We modify a class of multivariate tests with elliptical confidence regions, not necessarily arising from normal-based distribution theory. The resulting statistics are easy to compute, they do not require the re-estimation of models subject to one-sided inequality restrictions, and their distributions do not require bounds-based inference. We derive exact explicit distributions, then prove some desirable properties of our class of modified tests. We then illustrate the relevance of the method by applying it to devising an improved test of random walks in autoregressive models with deterministic components. In this example, the usual alternative to a unit root is one-sided in the direction of stable roots, while deterministic components are allowed to go either way, and we show that it is beneficial to take the partially one-sided nature of the alternative into account.

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Bibliographic Info

Paper provided by Department of Economics, University of York in its series Discussion Papers with number 05/13.

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Handle: RePEc:yor:yorken:05/13

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Postal: Department of Economics and Related Studies, University of York, York, YO10 5DD, United Kingdom
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Cited by:
  1. Peter Martey Addo & Monica Billio & Dominique Guegan, 2011. "A test for a new modelling: The Univariate MT-STAR Model," Documents de travail du Centre d'Economie de la Sorbonne 11083, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  2. Joakim Westerlund, . "Heteroskedasticity Robust Panel Unit Root tests," Financial Econometics Series 2014_02, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance.
  3. Elena Andreou & Bas J.M. Werker, 2014. "Residual-based Rank Specification Tests for AR-GARCH type models," University of Cyprus Working Papers in Economics 02-2014, University of Cyprus Department of Economics.
  4. Gozbasi, Onur & Kucukkaplan, Ilhan & Nazlioglu, Saban, 2014. "Re-examining the Turkish stock market efficiency: Evidence from nonlinear unit root tests," Economic Modelling, Elsevier, vol. 38(C), pages 381-384.
  5. Juan Carlos Cuestas & Paulo José Regis, 2010. "Purchasing power parity in OECD countries: nonlinear unit root tests revisited," Working Papers 2010/3, Nottingham Trent University, Nottingham Business School, Economics Division.
  6. repec:hal:journl:halshs-00659158 is not listed on IDEAS
  7. Grote, Claudia & Sibbertsen, Philipp, 2013. "Testing for Cointegration in a Double-LSTR Framework," Hannover Economic Papers (HEP) dp-514, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  8. Cuestas, Juan C. & Gil-Alana, Luis A. & Staehr, Karsten, 2011. "A further investigation of unemployment persistence in European transition economies," Journal of Comparative Economics, Elsevier, vol. 39(4), pages 514-532.
  9. Juan Cuestas & Dean Garratt, 2011. "Is real GDP per capita a stationary process? Smooth transitions, nonlinear trends and unit root testing," Empirical Economics, Springer, vol. 41(3), pages 555-563, December.
  10. Westerlund, Joakim & Larsson, Rolf, 2012. "Testing for a unit root in a random coefficient panel data model," Journal of Econometrics, Elsevier, vol. 167(1), pages 254-273.
  11. Robinson Kruse, 2011. "A new unit root test against ESTAR based on a class of modified statistics," Statistical Papers, Springer, vol. 52(1), pages 71-85, February.
  12. Angelov, Nikolay, 2006. "Structural breaks in Iron-Ore prices: The impact of the 1973 oil crisis," Working Paper Series 2006:11, Uppsala University, Department of Economics.
  13. Distaso, Walter, 2008. "Testing for unit root processes in random coefficient autoregressive models," Journal of Econometrics, Elsevier, vol. 142(1), pages 581-609, January.
  14. Chen, Shyh-Wei, 2014. "Smooth transition, non-linearity and current account sustainability: Evidence from the European countries," Economic Modelling, Elsevier, vol. 38(C), pages 541-554.

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