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Testing for Co-integration in Vector Autoregressions with Non-Stationary Volatility

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  • Giuseppe Cavaliere

    (Department of Statistical Sciences, University of Bologna)

  • Anders Rahbek

    (Department of Economics, University of Copenhagen)

  • A. M. Robert Taylor

    (University of Nottingham)

Abstract

Many key macro-economic and ?nancial variables are characterised by permanent changes in unconditional volatility. In this paper we analyse vector autoregressions with non-stationary (unconditional) volatility of a very general form, which includes single and multiple volatility breaks as special cases. We show that the conventional rank statistics computed as in Johansen (1988,1991) are potentially unreliable. In particular, their large sample distributions depend on the integrated covariation of the underlying multivariate volatility process which impacts on both the size and power of the associated co-integration tests, as we demonstrate numerically. A solution to the identi?ed inference problem is provided by considering wild bootstrap-based implementations of the rank tests. These do not require the practitioner to specify a parametric model for volatility, nor to assume that the pattern of volatility is common to, or independent across, the vector of series under analysis. The bootstrap is shown to perform very well in practice.

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Bibliographic Info

Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 08-34.

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Length: 28 pages
Date of creation: Sep 2008
Date of revision:
Handle: RePEc:kud:kuiedp:0834

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Keywords: co-integration; non-stationary volatility; trace and maximum eigenvalue tests; wild bootstrap;

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Cited by:
  1. Marçal, Emerson Fernandes, 2013. "Exchange rate misalignments, interdependence, crises, and currency wars: an empirical assessment," Textos para discussão 348, Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
  2. Kascha, Christian & Trenkler, Carsten, 2011. "Bootstrapping the likelihood ratio cointegration test in error correction models with unknown lag order," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1008-1017, February.
  3. Giuseppe Cavaliere & Anders Rahbek & A.M.Robert Taylor, 2009. "Co-integration Rank Testing under Conditional Heteroskedasticity," CREATES Research Papers 2009-22, School of Economics and Management, University of Aarhus.
  4. Majid M. Al-Sadoon, 2014. "A general theory of rank testing," Economics Working Papers 1411, Department of Economics and Business, Universitat Pompeu Fabra.
  5. Guiseppe Cavaliere & Anders Rahbek & A.M.Robert Taylor, 2010. "Bootstrap Sequential Determination of the Co-integration Rank in VAR Models," CREATES Research Papers 2010-07, School of Economics and Management, University of Aarhus.
  6. Herwartz, H. & Siedenburg, F., 2008. "Homogenous panel unit root tests under cross sectional dependence: Finite sample modifications and the wild bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 137-150, September.
  7. Christoph Hanck & Robert Czudaj, 2013. "Nonstationary-Volatility Robust Panel Unit Root Tests and the Great Moderation," Ruhr Economic Papers 0434, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
  8. Cavaliere, Giuseppe & Taylor, A. M. Robert & Trenkler, Carsten, 2013. "Bootstrap Co-integration Rank Testing: The Effect of Bias-Correcting Parameter Estimates," Working Papers 32993, University of Mannheim, Department of Economics.
  9. Hanck, Christoph & Demetrescu, Matei & Tarcolea, Adina, 2012. "IV-Based Cointegration Testing in Dependent Panels with Time-Varying Variance," Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 62072, Verein für Socialpolitik / German Economic Association.
  10. Giuseppe Cavaliere & Anders Rahbek & A. M. Robert Taylor, 2009. "Co-integration rank tests under conditional heteroskedasticity," Discussion Papers 09/02, University of Nottingham, Granger Centre for Time Series Econometrics.
  11. Daniela Osterrieder, 2013. "Interest Rates with Long Memory: A Generalized Affine Term-Structure Model," CREATES Research Papers 2013-17, School of Economics and Management, University of Aarhus.
  12. Xu, Ke-Li, 2012. "Robustifying multivariate trend tests to nonstationary volatility," Journal of Econometrics, Elsevier, vol. 169(2), pages 147-154.
  13. Matei Demetrescu & Christoph Hanck, 2013. "Nonlinear IV panel unit root testing under structural breaks in the error variance," Statistical Papers, Springer, vol. 54(4), pages 1043-1066, November.
  14. Bec, Frédérique & Gollier, Christian, 2009. "Cyclicality and Term Structure of Value-at-Risk in Europe," TSE Working Papers 09-035, Toulouse School of Economics (TSE).
  15. Emerson Fernandes Marçal & Priscila Fernandes Ribeiro, 2011. "Levado pelos Fundamentos? Estimando o Desalinhamento Cambial Norte-Americano a partir de Técnicas de Cointegração," Discussion Papers 1674, Instituto de Pesquisa Econômica Aplicada - IPEA.
  16. Marçal, Emerson Fernandes & Valls Pereira, Pedro L., 2012. "Evaluating the existence of structural change in the brazilian term structure of interest : evidence based on cointegration models with structural break," Textos para discussão 314, Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
  17. Boswijk, H. P. & Zu, Y., 2013. "Testing for Cointegration with Nonstationary Volatility," Working Papers 13/08, Department of Economics, City University London.
  18. Corbo, Vesna & Osbat, Chiara, 2012. "Optimism bias? The elasticity puzzle in international economics revisited," Working Paper Series 1482, European Central Bank.
  19. Emerson Fernandes Marçal & Fernando Barbi, 2010. "“Quo Vadis Real? Estimating the Brazilian Real Exchange Rate Misalignment in Vector Error Correction Model with Structural Change”," Working Papers 10-2010, Universidade de São Paulo, Faculdade de Economia, Administração e Contabilidade de Ribeirão Preto.

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