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Tests of time-invariance

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  • Busettti, F.
  • Harvey, A.

Abstract

Quantiles provide a comprehensive description of the properties of a variable and tracking changes in quantiles over time using signal extraction methods can be informative. It is shown here how stationarity tests can be generalized to test the null hypothesis that a particular quantile is constant over time by using weighted indicators. Corresponding tests based on expectiles are also proposed; these might be expected to be more powerful for distributions that are not heavy-tailed. Tests for changing dispersion and asymmetry may be based on contrasts between particular quantiles or expectiles. We report Monte Carlo experiments investigating the e¤ectiveness of the proposed tests and then move on to consider how to test for relative time invariance, based on residuals from fitting a time-varying level or trend. Empirical examples, using stock returns and U.S. inflation, provide an indication of the practical importance of the tests.

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Bibliographic Info

Paper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 0657.

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Length: 29
Date of creation: Mar 2007
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Handle: RePEc:cam:camdae:0657

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Related research

Keywords: Dispersion; expectiles; quantiles; skewness; stationarity tests; stochastic volatility; value at risk.;

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References

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  1. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, Econometric Society, vol. 59(3), pages 817-58, May.
  2. Robert Engle & Simone Manganelli, 2000. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Econometric Society World Congress 2000 Contributed Papers 0841, Econometric Society.
  3. Neil Shephard, 2005. "Stochastic volatility," Economics Series Working Papers 2005-W17, University of Oxford, Department of Economics.
  4. Harvey, A.C. & Koopman, S.J.M., 1999. "Signal Extraction and the Formulation of Unobserved Components Models," Discussion Paper, Tilburg University, Center for Economic Research 1999-44, Tilburg University, Center for Economic Research.
  5. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780198523543, October.
  6. Andrew Harvey & Jared Bernstein, 2003. "Measurement and Testing of Inequality from Time Series of Deciles with an Application to U.S. Wages," The Review of Economics and Statistics, MIT Press, vol. 85(1), pages 141-152, February.
  7. Jukka Nyblom & Andrew Harvey, 2001. "Testing against smooth stochastic trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 16(3), pages 415-429.
  8. Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 979, Cowles Foundation for Research in Economics, Yale University.
  9. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 15(03), pages 269-298, June.
  10. Koopman, S.J.M. & Shephard, N. & Doornik, J.A., 1998. "Statistical Algorithms for Models in State Space Using SsfPack 2.2," Discussion Paper, Tilburg University, Center for Economic Research 1998-141, Tilburg University, Center for Economic Research.
  11. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, Econometric Society, vol. 55(4), pages 819-47, July.
  12. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2005. "Stationarity Tests Under Time-Varying Second Moments," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 21(06), pages 1112-1129, December.
  13. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 34(04), pages 465-487, December.
  14. Nyblom, Jukka & Harvey, Andrew, 2000. "Tests Of Common Stochastic Trends," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 16(02), pages 176-199, April.
  15. Linton, O. & Whang, Yoon-Jae, 2007. "The quantilogram: With an application to evaluating directional predictability," Journal of Econometrics, Elsevier, Elsevier, vol. 141(1), pages 250-282, November.
  16. de Jong, Robert M. & Amsler, Christine & Schmidt, Peter, 2007. "A robust version of the KPSS test based on indicators," Journal of Econometrics, Elsevier, Elsevier, vol. 137(2), pages 311-333, April.
  17. DeRossi, G. & Harvey, A., 2006. "Time-Varying Quantiles," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 0649, Faculty of Economics, University of Cambridge.
  18. Harvey, Andrew & Streibel, Mariane, 1998. "Testing for a slowly changing level with special reference to stochastic volatility," Journal of Econometrics, Elsevier, Elsevier, vol. 87(1), pages 167-189, August.
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Citations

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Cited by:
  1. DeRossi, G. & Harvey, A., 2007. "Quantiles, Expectiles and Splines," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 0660, Faculty of Economics, University of Cambridge.
  2. George Kapetanios, 2007. "Testing for Strict Stationarity," Working Papers, Queen Mary, University of London, School of Economics and Finance 602, Queen Mary, University of London, School of Economics and Finance.
  3. Fabio Busetti & Andrew Harvey, 2011. "When is a Copula Constant? A Test for Changing Relationships," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(1), pages 106-131, Winter.
  4. Harvey, A., 2008. "Dynamic distributions and changing copulas," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 0839, Faculty of Economics, University of Cambridge.

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