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Cointegration Rank Testing Under Conditional Heteroskedasticity

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

Abstract

We analyse the properties of the conventional Gaussian-based co-integrating rank tests of Johansen (1996) in the case where the vector of series under test is driven by globally stationary, conditionally heteroskedastic (martingale differ- ence) innovations. We first demonstrate that the limiting null distributions of the rank statistics coincide with those derived by previous authors who assume either i.i.d. or (strict and covariance) stationary martingale difference innovations. We then propose wild bootstrap implementations of the co-integrating rank tests and demonstrate that the associated bootstrap rank statistics replicate the first-order asymptotic null distributions of the rank statistics. We show the same is also true of the corresponding rank tests based on the i.i.d. bootstrap of Swensen (2006). The wild bootstrap, however, has the important property that, unlike the i.i.d. bootstrap, it preserves in the re-sampled data the pattern of heteroskedasticity present in the original shocks. Consistent with this, numerical evidence sug- gests that, relative to tests based on the asymptotic critical values or the i.i.d. bootstrap, the wild bootstrap rank tests perform very well in small samples un- der a variety of conditionally heteroskedastic innovation processes. An empirical application to the term structure of interest rates is given.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 26 (2010)
Issue (Month): 06 (December)
Pages: 1719-1760

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Handle: RePEc:cup:etheor:v:26:y:2010:i:06:p:1719-1760_99

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Citations

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Cited by:
  1. Mezgebo, Taddese, 2009. "A multivariate approach for identification of optimal locations with in Ethiopia’s wheat market to tackle soaring inflation on food price (Extended version)," MPRA Paper 17960, University Library of Munich, Germany.
  2. Majid M. Al-Sadoon, 2014. "A general theory of rank testing," Economics Working Papers 1411, Department of Economics and Business, Universitat Pompeu Fabra.
  3. Brüggemann, Ralf & Jentsch, Carsten & Trenkler, Carsten, 2014. "Inference in VARs with Conditional Heteroskedasticity of Unknown Form," Working Papers, University of Mannheim, Department of Economics 14-21, University of Mannheim, Department of Economics.
  4. Bicu Andreea & Candelon Bertrand, 2012. "Government bond market dynamics and sovereign risk: systemic or idiosyncratic?," Research Memorandum 032, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  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. Cavaliere, Giuseppe & Rahbek, Anders & Taylor, Robert, 2010. "Determination of the Number of Common Stochastic Trends Under Conditional Heteroskedasticity/Determinación del número de tendencias estocásticas comunes bajo heteroscedasticidad condicional," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 28, pages 519-552, Diciembre.
  7. Giuseppe Cavaliere & A. M. Robert Taylor & Carsten Trenkler, 2010. "Bootstrap co-integration rank testing: the role of deterministic variables and initial values in the bootstrap recursion," Discussion Papers, University of Nottingham, Granger Centre for Time Series Econometrics 10/04, University of Nottingham, Granger Centre for Time Series Econometrics.
  8. Jentsch, Carsten & Paparoditis, Efstathios & Politis, Dimitris N., 2014. "Block Bootstrap Theory for Multivariate Integrated and Cointegrated Processes," Working Papers, University of Mannheim, Department of Economics 14-18, University of Mannheim, Department of Economics.
  9. Christian Kascha & Carsten Trenkler, 2011. "Cointegrated VARMA models and forecasting US interest rates," ECON - Working Papers, Department of Economics - University of Zurich 033, Department of Economics - University of Zurich.
  10. Corbo, Vesna & Osbat, Chiara, 2012. "Optimism bias? The elasticity puzzle in international economics revisited," Working Paper Series, European Central Bank 1482, European Central Bank.
  11. Li, Yingzi & Fortenbery, T. Randall, 2013. "Do Speculators in Futures Markets Make Cash Markets More Volatile?," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C., Agricultural and Applied Economics Association 151296, Agricultural and Applied Economics Association.
  12. Phillips, Peter C.B. & Magdalinos, Tassos, 2013. "Inconsistent Var Regression With Common Explosive Roots," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 29(04), pages 808-837, August.
  13. Anders Rahbek & Heino Bohn Nielsen, 2012. "Unit root vector autoregression with volatility induced stationarity," Discussion Papers 12-02, University of Copenhagen. Department of Economics.
  14. Cavaliere, Giuseppe & Taylor, A. M. Robert & Trenkler, Carsten, 2013. "Bootstrap Co-integration Rank Testing: The Effect of Bias-Correcting Parameter Estimates," Working Papers, University of Mannheim, Department of Economics 32993, University of Mannheim, Department of Economics.
  15. Łukasz Goczek & Dagmara Mycielska, 2013. "Ready for euro? Empirical study of the actual monetary policy independence in Poland," Working Papers 2013-13, Faculty of Economic Sciences, University of Warsaw.

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