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Co-integration Rank Testing under Conditional Heteroskedasticity

Author

Listed:
  • Giuseppe Cavaliere

    () (Department of Statistical Sciences, University of Bologna)

  • Anders Rahbek

    () (Department of Economics, University of Copenhagen and CREATES)

  • A.M.Robert Taylor

    () (School of Economics and Granger Centre for Time Series Econometrics, University of Nottingham)

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 difference) 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 suggests 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 under a variety of conditionally heteroskedastic innovation processes. An empirical application to the term structure of interest rates is given.

Suggested Citation

  • Giuseppe Cavaliere & Anders Rahbek & A.M.Robert Taylor, 2009. "Co-integration Rank Testing under Conditional Heteroskedasticity," CREATES Research Papers 2009-22, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2009-22
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    References listed on IDEAS

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    Keywords

    Co-integration; trace and maximum eigenvalue rank tests; conditional heteroskedasticity; i.i.d. bootstrap; wild bootstrap;

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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