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Unit root tests under time-varying variances

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  • Giuseppe Cavaliere

Abstract

The paper provides a general framework for investigating the effects of permanent changes in the variance of the errors of an autoregressive process on unit root tests. Such a framework — which is based on a novel asymptotic theory for integrated and near integrated processes with heteroskedastic errors — allows to evaluate how the variance dynamics affect the size and the power function of unit root tests. Contrary to previous studies, it is shown that under permanent variance shifts, the conventional critical values can lead both to oversized and undersized tests. The paper concludes by showing that the power function of the unit root tests is affected by non-constant variances as well.

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Bibliographic Info

Paper provided by Department of Statistics, University of Bologna in its series Quaderni di Dipartimento with number 2.

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Date of creation: 2003
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Handle: RePEc:bot:quadip:89

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Cited by:
  1. Barbara Rossi & Tatevik Sekhposyany, 2014. "Forecast Rationality Tests in the Presence of Instabilities, With Applications to Federal Reserve and Survey Forecasts," Working Papers 765, Barcelona Graduate School of Economics.
  2. Giuseppe Cavaliere & Morten Ørregaard Nielsen & A.M. Robert Taylor, 2013. "Bootstrap Score Tests for Fractional Integration in Heteroskedastic ARFIMA Models, with an Application to Price Dynamics in Commodity Spot and Futures Markets," Working Papers 1309, Queen's University, Department of Economics.
  3. Simões, Oscar R. & Marçal, Emerson Fernandes, 2012. "Agregação temporal e não-linearidade afetam os testes da Paridade do Poder de compra: Evidência a partir de dados brasileiros," Textos para discussão 310, Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
  4. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2008. "Testing for a change in persistence in the presence of non-stationary volatility," Journal of Econometrics, Elsevier, vol. 147(1), pages 84-98, November.
  5. Giuseppe Cavaliere & David I. Harvey & Stephen J. Leybourne & A.M. Robert Taylor, 2008. "Testing for Unit Roots in the Presence of a Possible Break in Trend and Non-Stationary Volatility," CREATES Research Papers 2008-62, School of Economics and Management, University of Aarhus.
  6. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2007. "Testing for unit roots in time series models with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 140(2), pages 919-947, October.
  7. Atiq-ur-Rehman, Atiq-ur-Rehman & Zaman, Asad, 2009. "Impact of Model Specification Decisions on Unit Root Tests," MPRA Paper 19963, University Library of Munich, Germany.
  8. Giuseppe Cavaliere & Anders Rahbek & A.M.Robert Taylor, 2008. "Testing for Co-integration in Vector Autoregressions with Non-Stationary Volatility," CREATES Research Papers 2008-50, School of Economics and Management, University of Aarhus.
  9. Barbara Rossi & Tatevik Sekhposyan, 2014. "Forecast rationality tests in the presence of instabilities, with applications to Federal Reserve and survey forecasts," Economics Working Papers 1426, Department of Economics and Business, Universitat Pompeu Fabra.
  10. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2012. "Unit roots, nonlinearities and structural breaks," CREATES Research Papers 2012-14, School of Economics and Management, University of Aarhus.
  11. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2005. "Stationarity Tests Under Time-Varying Second Moments," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1112-1129, December.
  12. Rodrigues, Paulo M.M. & Rubia, Antonio, 2007. "Testing for causality in variance under nonstationarity in variance," Economics Letters, Elsevier, vol. 97(2), pages 133-137, November.
  13. Brandan K. Beare, 2008. "Unit Root Testing with Unstable Volatility," Economics Series Working Papers 2008-WO6, University of Oxford, Department of Economics.
  14. VAN BELLEGEM, Sébastien, 2011. "Locally stationary volatility modelling," CORE Discussion Papers 2011041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  15. Boswijk, H. P. & Zu, Y., 2013. "Testing for Cointegration with Nonstationary Volatility," Working Papers 13/08, Department of Economics, City University London.
  16. Kourogenis, Nikolaos & Pittis, Nikitas, 2008. "Cointegration, variance shifts and the limiting distribution of the OLS estimator," Economics Letters, Elsevier, vol. 99(1), pages 103-106, April.
  17. Atiq-ur-Rehman, Atiq-ur-Rehman & Zaman, Asad, 2008. "Model specification, observational equivalence and performance of unit root tests," MPRA Paper 13489, University Library of Munich, Germany.

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