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

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  • Giuseppe Cavaliere
  • Anders Rahbek
  • A.M.Robert Taylor

    ()
    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract

Many key macro-economic and financial 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 identified 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 School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2008-50.

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Length: 37
Date of creation: 08 Sep 2008
Date of revision:
Handle: RePEc:aah:create:2008-50

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Web page: http://www.econ.au.dk/afn/

Related research

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

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References

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Cited by:
  1. Bec, Frédérique & Gollier, Christian, 2009. "Cyclicality and Term Structure of Value-at-Risk in Europe," IDEI Working Papers 587, Institut d'Économie Industrielle (IDEI), Toulouse.
  2. Giuseppe Cavaliere & Anders Rahbek & A. M. Robert Taylor, 2010. "Bootstrap Sequential Determination of the Co-integration Rank in VAR Models," Discussion Papers 10-07, University of Copenhagen. Department of Economics.
  3. 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).
  4. 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.
  5. 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.
  6. Cavaliere, Giuseppe & Rahbek, Anders & Taylor, A.M. Robert, 2010. "Cointegration Rank Testing Under Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 26(06), pages 1719-1760, December.
  7. Czudaj, Robert & Hanck, Christoph, 2013. "Nonstationary-Volatility Robust Panel Unit Root Tests and the Great Moderation," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79734, Verein für Socialpolitik / German Economic Association.
  8. 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.
  9. Xu, Ke-Li, 2012. "Robustifying multivariate trend tests to nonstationary volatility," Journal of Econometrics, Elsevier, vol. 169(2), pages 147-154.
  10. Boswijk, H. P. & Zu, Y., 2013. "Testing for Cointegration with Nonstationary Volatility," Working Papers 13/08, Department of Economics, City University London.
  11. Majid M. Al-Sadoon, 2014. "A general theory of rank testing," Economics Working Papers 1411, Department of Economics and Business, Universitat Pompeu Fabra.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  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. 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.
  18. 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.
  19. Corbo, Vesna & Osbat, Chiara, 2012. "Optimism bias? The elasticity puzzle in international economics revisited," Working Paper Series 1482, European Central Bank.

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