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Time-Varying Quantiles

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Author Info

  • DeRossi, G.
  • Harvey, A.

Abstract

A time-varying quantile can be fitted to a sequence of observations by formulating a time series model for the corresponding population quantile and iteratively applying a suitably modified state space signal extraction algorithm. Quantiles estimated in this way provide information on various aspects of a time series, including dispersion, asymmetry and, for financial applications, value at risk. Tests for the constancy of quantiles, and associated contrasts, are constructed using indicator variables; these tests have a similar form to stationarity tests and, under the null hypothesis, their asymptotic distributions belong to the Cramér von Mises family. Estimates of the quantiles at the end of the series provide the basis for forecasting. As such they offer an alternative to conditional quantile autoregressions and, at the same time, give some insight into their structure and potential drawbacks.

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File URL: http://www.econ.cam.ac.uk/research/repec/cam/pdf/cwpe0649.pdf
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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 0649.

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Length: 42
Date of creation: Jul 2006
Date of revision:
Handle: RePEc:cam:camdae:0649

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Related research

Keywords: Dispersion; quantile regression; signal extraction; state space smoother; stationarity tests; value at risk.;

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References

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  1. James W. Taylor, 2005. "Generating Volatility Forecasts from Value at Risk Estimates," Management Science, INFORMS, vol. 51(5), pages 712-725, May.
  2. Komunjer, Ivana, 2002. "Quasi-Maximum Likelihood Estimation for Conditional Quantiles," Working Papers 1139, California Institute of Technology, Division of the Humanities and Social Sciences.
  3. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "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?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
  4. 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.
  5. de Jong, Robert M. & Amsler, Christine & Schmidt, Peter, 2007. "A robust version of the KPSS test based on indicators," Journal of Econometrics, Elsevier, vol. 137(2), pages 311-333, April.
  6. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543, September.
  7. Len Umantsev & Victor Chernozhukov, 2001. "Conditional value-at-risk: Aspects of modeling and estimation," Empirical Economics, Springer, vol. 26(1), pages 271-292.
  8. Jukka Nyblom & Andrew Harvey, 2001. "Testing against smooth stochastic trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 415-429.
  9. Neil Shephard & Jurgen Doornik & Siem Jan Koopman, 1998. "Statistical algorithms for models in state space using SsfPack 2.2," Economics Series Working Papers 1998-W06, University of Oxford, Department of Economics.
  10. Harvey, Andrew, 2006. "Forecasting with Unobserved Components Time Series Models," Handbook of Economic Forecasting, Elsevier.
  11. repec:cup:etheor:v:12:y:1996:i:5:p:793-813 is not listed on IDEAS
  12. Andrew Harvey & Siem Jan Koopman, 2000. "Signal extraction and the formulation of unobserved components models," Econometrics Journal, Royal Economic Society, vol. 3(1), pages 84-107.
  13. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-47, July.
  14. Linton, O. & Whang, Yoon-Jae, 2007. "The quantilogram: With an application to evaluating directional predictability," Journal of Econometrics, Elsevier, vol. 141(1), pages 250-282, November.
  15. Donald W.K. Andrews, 1999. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Cowles Foundation Discussion Papers 1229, Cowles Foundation for Research in Economics, Yale University.
  16. Bosch, Ronald J. & Ye, Yinyu & Woodworth, George G., 1995. "A convergent algorithm for quantile regression with smoothing splines," Computational Statistics & Data Analysis, Elsevier, vol. 19(6), pages 613-630, June.
  17. Engle, Robert F & Manganelli, Simone, 1999. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," University of California at San Diego, Economics Working Paper Series qt06m3d6nv, Department of Economics, UC San Diego.
  18. Peter Christoffersen & Jinyong Hahn & Atsushi Inoue, 2001. "Testing and Comparing Value-at-Risk Measures," CIRANO Working Papers 2001s-03, CIRANO.
  19. Neil Shephard, 2005. "Stochastic volatility," Economics Series Working Papers 2005-W17, University of Oxford, Department of Economics.
  20. Koenker, Roger & Zhao, Quanshui, 1996. "Conditional Quantile Estimation and Inference for Arch Models," Econometric Theory, Cambridge University Press, vol. 12(05), pages 793-813, December.
  21. J. Durbin & S. J. Koopman, 2000. "Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 3-56.
  22. Harvey, Andrew & Streibel, Mariane, 1998. "Testing for a slowly changing level with special reference to stochastic volatility," Journal of Econometrics, Elsevier, vol. 87(1), pages 167-189, August.
  23. Keith Kuester & Stefan Mittnik & Marc S. Paolella, 2006. "Value-at-Risk Prediction: A Comparison of Alternative Strategies," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 53-89.
  24. Koenker, Roger & Xiao, Zhijie, 2006. "Quantile Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 980-990, September.
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Citations

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Cited by:
  1. Harvey, Andrew, 2010. "Tracking a changing copula," Journal of Empirical Finance, Elsevier, vol. 17(3), pages 485-500, June.
  2. Busetti, F. & Harvey, A., 2008. "When is a copula constant? A test for changing relationships," Cambridge Working Papers in Economics 0841, Faculty of Economics, University of Cambridge.
  3. De Rossi, Giuliano & Harvey, Andrew, 2009. "Quantiles, expectiles and splines," Journal of Econometrics, Elsevier, vol. 152(2), pages 179-185, October.
  4. Clive Bowsher & Roland Meeks, 2008. "The Dynamics of Economic Functions: Modelling and Forecasting the Yield Curve," OFRC Working Papers Series 2008fe24, Oxford Financial Research Centre.
  5. Busettti, F. & Harvey, A., 2007. "Tests of time-invariance," Cambridge Working Papers in Economics 0701, Faculty of Economics, University of Cambridge.
  6. Harvey, A., 2008. "Dynamic distributions and changing copulas," Cambridge Working Papers in Economics 0839, Faculty of Economics, University of Cambridge.
  7. Maria Rosa Nieto & Esther Ruiz, 2008. "Measuring financial risk : comparison of alternative procedures to estimate VaR and ES," Statistics and Econometrics Working Papers ws087326, Universidad Carlos III, Departamento de Estadística y Econometría.

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