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Bootstrap LR tests of stationarity, common trends and cointegration

  • Fabio Busetti

    ()

    (Bank of Italy)

  • Silvestro di Sanzo

    ()

    (Confcommercio)

The paper considers likelihood ratio (LR) tests of stationarity, common trends and cointegration for multivariate time series. As the distribution of these tests is not known, a bootstrap version is proposed via a state space representation. The bootstrap samples are obtained from the Kalman filter innovations under the null hypothesis. Monte Carlo simulations for the Gaussian univariate random walk plus noise model show that the bootstrap LR test achieves higher power for medium-sized deviations from the null hypothesis than a locally optimal and one-sided LM test, that has a known asymptotic distribution. The power gains of the bootstrap LR test are significantly larger for testing the hypothesis of common trends and cointegration in multivariate time series, as the alternative asymptotic procedure -obtained as an extension of the LM test of stationarity- does not possess properties of optimality. Finally, it is showed that the (pseudo) LR tests maintain good size and power properties also for non-Gaussian series. As an empirical illustration, we find evidence of two common stochastic trends in the volatility of the US dollar exchange rate against european and asian/pacific currencies.

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Paper provided by Bank of Italy, Economic Research and International Relations Area in its series Temi di discussione (Economic working papers) with number 799.

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Date of creation: Mar 2011
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Handle: RePEc:bdi:wptemi:td_799_11
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  1. A. W. Coats, 1996. "Introduction," History of Political Economy, Duke University Press, vol. 28(5), pages 3-11, Supplemen.
  2. Busetti, Fabio & Harvey, Andrew, 2003. "Seasonality Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 420-36, July.
  3. Russell Davidson & James G. MacKinnon, 2004. "The Power of Bootstrap and Asymptotic Tests," Working Papers 1035, Queen's University, Department of Economics.
  4. Burridge, Peter & Robert Taylor, A. M., 2004. "Bootstrapping the HEGY seasonal unit root tests," Journal of Econometrics, Elsevier, vol. 123(1), pages 67-87, November.
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  6. Fabio Busetti, 2004. "Tests of seasonal integration and cointegration in multivariate unobserved component models," Econometrics 0411003, EconWPA.
  7. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589826.
  8. Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation for Research in Economics, Yale University.
  9. Kilian, L. & Caner, M., 1999. "Size Distortions of Tests of the Null Hypothesis of Stationarity: Evidence and Implications for the PPP Debate," Papers 99-05, Michigan - Center for Research on Economic & Social Theory.
  10. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589819.
  11. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589833.
  12. Canova, Fabio & Hansen, Bruce E, 1995. "Are Seasonal Patterns Constant over Time? A Test for Seasonal Stability," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 237-52, July.
  13. Lee, Junsoo, 1996. "On the power of stationarity tests using optimal bandwidth estimates," Economics Letters, Elsevier, vol. 51(2), pages 131-137, May.
  14. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, EconWPA, revised 05 Mar 1996.
  15. James G. MacKinnon, 2006. "Bootstrap Methods in Econometrics," Working Papers 1028, Queen's University, Department of Economics.
  16. Jeremy Berkowitz & Lutz Kilian, 2000. "Recent developments in bootstrapping time series," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 1-48.
  17. Leybourne, S J & McCabe, B P M, 1994. "A Consistent Test for a Unit Root," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 157-66, April.
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  19. Donald W. K. Andrews, 2000. "Inconsistency of the Bootstrap when a Parameter Is on the Boundary of the Parameter Space," Econometrica, Econometric Society, vol. 68(2), pages 399-406, March.
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