Time-Varying Quantiles

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Time-Varying Quantiles

Author Info

DeRossi, G.
Harvey, A.

Additional information is available for the following registered author(s):

Andrew C. Harvey

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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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
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Handle: RePEc:cam:camdae:0649

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Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

This paper has been announced in the following NEP Reports:

NEP-ALL-2006-07-28 (All new papers)
NEP-ECM-2006-07-28 (Econometrics)
NEP-ETS-2006-07-28 (Econometric Time Series)
NEP-FOR-2006-07-28 (Forecasting)
NEP-RMG-2006-07-28 (Risk Management)

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

Komunjer, Ivana, 2005. "Quasi-maximum likelihood estimation for conditional quantiles," Journal of Econometrics, Elsevier, vol. 128(1), pages 137-164, September. [Downloadable!] (restricted)
Other versions:
- Komunjer, Ivana, 2002. "Quasi-Maximum Likelihood Estimation for Conditional Quantiles," Working Papers 1139, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
Christoffersen, Peter & Hahn, Jinyong & Inoue, Atsushi, 2001. "Testing and comparing Value-at-Risk measures," Journal of Empirical Finance, Elsevier, vol. 8(3), pages 325-342, July. [Downloadable!] (restricted)
Other versions:
- Peter Christoffersen & Jinyong Hahn & Atsushi Inoue, 2001. "Testing and Comparing Value-at-Risk Measures," CIRANO Working Papers 2001s-03, CIRANO. [Downloadable!]
Durbin, J. & Koopman, S.J., 1998. "Time series analysis of non-gaussian observations based on state space models from both classical and bayesian perspectives," Discussion Paper 142, Tilburg University, Center for Economic Research. [Downloadable!]
Other versions:
- 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. [Downloadable!] (restricted)
Koenker, Roger & Xiao, Zhijie, 2006. "Quantile Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 980-990, September. [Downloadable!] (restricted)
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. [Downloadable!]
Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
Harvey, Andrew, 2006. "Forecasting with Unobserved Components Time Series Models," Handbook of Economic Forecasting, Elsevier. [Downloadable!] (restricted)
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, 08. [Downloadable!] (restricted)
Other versions:
- Jared Bernstein & Andrew Harvey, 2000. "Measurement and Testing of Inequality from Time Series of Deciles with an Application to U.S. Wages," Econometric Society World Congress 2000 Contributed Papers 0861, Econometric Society. [Downloadable!]
Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
Other versions:
- Donald W.K. Andrews, 1999. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Cowles Foundation Discussion Papers 1229, Cowles Foundation, Yale University. [Downloadable!]
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. [Downloadable!] (restricted)
Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October. [Downloadable!] (restricted)
Other versions:
- Robert Engle & Simone Manganelli, 2000. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Econometric Society World Congress 2000 Contributed Papers 0841, Econometric Society. [Downloadable!]
- Robert Engle & Simone Manganelli, 1999. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," University of California at San Diego, Economics Working Paper Series 1999-20, Department of Economics, UC San Diego. [Downloadable!]
- Robert F. Engle & Simone Manganelli, 1999. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," University of California at San Diego, Economics Working Paper Series 99-20, Department of Economics, UC San Diego. [Downloadable!]
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. [Downloadable!] (restricted)
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. [Downloadable!] (restricted)
Other versions:
- 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 979, Cowles Foundation, Yale University. [Downloadable!]
- Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers 8905, Michigan State - Econometrics and Economic Theory.
repec:cup:etheor:v:12:y:1996:i:5:p:793-813 is not listed on IDEAS
Jukka Nyblom & Andrew Harvey, 2001. "Testing against smooth stochastic trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 415-429. [Downloadable!]
Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
Other versions:
- Koopman, S.J. & Shephard, N. & Doornik, J.A., 1998. "Statistical algorithms for models in state space using ssfpack 2.2," Discussion Paper 141, Tilburg University, Center for Economic Research. [Downloadable!]
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. [Downloadable!] (restricted)
Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-47, July. [Downloadable!] (restricted)
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.
Other versions:
- Harvey, A. & Koopman, S.J., 1999. "Signal extraction and the formulation of unobserved components models," Discussion Paper 44, Tilburg University, Center for Economic Research. [Downloadable!]

Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

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. [Downloadable!]
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. [Downloadable!]
DeRossi, G. & Harvey, A., 2007. "Quantiles, Expectiles and Splines," Cambridge Working Papers in Economics 0660, Faculty of Economics, University of Cambridge. [Downloadable!]
Other versions:
- DeRossi, G. & Harvey, A., 2007. "Quantiles, Expectiles and Splines," Cambridge Working Papers in Economics 0702, Faculty of Economics, University of Cambridge. [Downloadable!]
- De Rossi, Giuliano & Harvey, Andrew, 2009. "Quantiles, expectiles and splines," Journal of Econometrics, Elsevier, vol. 152(2), pages 179-185, October. [Downloadable!] (restricted)
Busettti, F. & Harvey, A., 2007. "Tests of time-invariance," Cambridge Working Papers in Economics 0657, Faculty of Economics, University of Cambridge. [Downloadable!]
Other versions:
- Busettti, F. & Harvey, A., 2007. "Tests of time-invariance," Cambridge Working Papers in Economics 0701, Faculty of Economics, University of Cambridge. [Downloadable!]
Harvey, A., 2008. "Dynamic distributions and changing copulas," Cambridge Working Papers in Economics 0839, Faculty of Economics, University of Cambridge. [Downloadable!]

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