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Time-Varying Quantiles

Author

Listed:
  • 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.

Suggested Citation

  • DeRossi, G. & Harvey, A., 2006. "Time-Varying Quantiles," Cambridge Working Papers in Economics 0649, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:0649
    Note: Ec
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    References listed on IDEAS

    as
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    9. 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.
    10. 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.
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    25. Jukka Nyblom & Andrew Harvey, 2001. "Testing against smooth stochastic trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 415-429.
    26. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Nieto, María Rosa, 2008. "Measuring financial risk : comparison of alternative procedures to estimate VaR and ES," DES - Working Papers. Statistics and Econometrics. WS ws087326, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Harvey, Andrew & Oryshchenko, Vitaliy, 2012. "Kernel density estimation for time series data," International Journal of Forecasting, Elsevier, vol. 28(1), pages 3-14.
    3. Ammy-Driss, Ayoub & Garcin, Matthieu, 2023. "Efficiency of the financial markets during the COVID-19 crisis: Time-varying parameters of fractional stable dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    4. Shuzhen Yang, 2021. "Compensatory model for quantile estimation and application to VaR," Papers 2112.07278, arXiv.org.
    5. Catania, Leopoldo & Luati, Alessandra, 2023. "Semiparametric modeling of multiple quantiles," Journal of Econometrics, Elsevier, vol. 237(2).
    6. Bowsher, Clive G. & Meeks, Roland, 2008. "The Dynamics of Economic Functions: Modeling and Forecasting the Yield Curve," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1419-1437.
    7. Fabio Busetti & Andrew Harvey, 2011. "When is a Copula Constant? A Test for Changing Relationships," Journal of Financial Econometrics, Oxford University Press, vol. 9(1), pages 106-131, Winter.
    8. De Rossi, Giuliano & Harvey, Andrew, 2009. "Quantiles, expectiles and splines," Journal of Econometrics, Elsevier, vol. 152(2), pages 179-185, October.
    9. Busettti, F. & Harvey, A., 2007. "Tests of time-invariance," Cambridge Working Papers in Economics 0701, Faculty of Economics, University of Cambridge.
    10. Caparoz, Marcel & Marçal, Emerson Fernandes & Mattos, Enlinson, 2019. "A time series analysis of household income inequality in Brazil 1977 to 2013," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 73(4), December.
    11. Pfarrhofer, Michael, 2022. "Modeling tail risks of inflation using unobserved component quantile regressions," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    12. Daniel Mariño-Ustacara & Luis Fernando Melo-Velandia, 2016. "Relación entre los valores en riesgo de los principales mercados financieros colombianos: un enfoque a través de modelos multivariados de regresión cuantílica," Borradores de Economia 975, Banco de la Republica de Colombia.
    13. Harvey, A., 2008. "Dynamic distributions and changing copulas," Cambridge Working Papers in Economics 0839, Faculty of Economics, University of Cambridge.
    14. Harvey, Andrew, 2010. "Tracking a changing copula," Journal of Empirical Finance, Elsevier, vol. 17(3), pages 485-500, June.

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    More about this item

    Keywords

    Dispersion; quantile regression; signal extraction; state space smoother; stationarity tests; value at risk.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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