IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v152y2009i2p179-185.html
   My bibliography  Save this article

Quantiles, expectiles and splines

Author

Listed:
  • De Rossi, Giuliano
  • Harvey, Andrew

Abstract

A time-varying quantile can be fitted by formulating a time series model for the corresponding population quantile and iteratively applying a suitably modified state space signal extraction algorithm. It is shown that such quantiles satisfy the defining property of fixed quantiles in having the appropriate number of observations above and below. Like quantiles, time-varying expectiles can be estimated by a state space signal extraction algorithm and they satisfy properties that generalize the moment conditions associated with fixed expectiles. Because the state space form can handle irregularly spaced observations, the proposed algorithms can be adapted to provide a viable means of computing spline-based non-parametric quantile and expectile regressions.

Suggested Citation

  • De Rossi, Giuliano & Harvey, Andrew, 2009. "Quantiles, expectiles and splines," Journal of Econometrics, Elsevier, vol. 152(2), pages 179-185, October.
  • Handle: RePEc:eee:econom:v:152:y:2009:i:2:p:179-185
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4076(09)00015-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Busettti, F. & Harvey, A., 2007. "Tests of time-invariance," Cambridge Working Papers in Economics 0701, Faculty of Economics, University of Cambridge.
    2. 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.
    3. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    4. 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.
    5. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    6. 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.
    7. DeRossi, G. & Harvey, A., 2006. "Time-Varying Quantiles," Cambridge Working Papers in Economics 0649, Faculty of Economics, University of Cambridge.
    8. 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.
    9. Jondeau, Eric & Rockinger, Michael, 2003. "Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1699-1737, August.
    10. 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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Busettti, F. & Harvey, A., 2007. "Tests of time-invariance," Cambridge Working Papers in Economics 0657, Faculty of Economics, University of Cambridge.
    2. DeRossi, G. & Harvey, A., 2006. "Time-Varying Quantiles," Cambridge Working Papers in Economics 0649, Faculty of Economics, University of Cambridge.
    3. Harvey, A., 2008. "Dynamic distributions and changing copulas," Cambridge Working Papers in Economics 0839, Faculty of Economics, University of Cambridge.
    4. Tommaso Proietti, 2002. "Some Reflections on Trend-Cycle Decompositions with Correlated Components," Econometrics 0209002, University Library of Munich, Germany.
    5. Fabio Busetti & Andrew Harvey, 2011. "When is a Copula Constant? A Test for Changing Relationships," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(1), pages 106-131, Winter.
    6. Hamidi, Benjamin & Maillet, Bertrand & Prigent, Jean-Luc, 2014. "A dynamic autoregressive expectile for time-invariant portfolio protection strategies," Journal of Economic Dynamics and Control, Elsevier, vol. 46(C), pages 1-29.
    7. Proietti, Tommaso, 2008. "Band spectral estimation for signal extraction," Economic Modelling, Elsevier, vol. 25(1), pages 54-69, January.
    8. Yuta Kurose & Yasuhiro Omori, 2012. "Bayesian Analysis of Time-Varying Quantiles Using a Smoothing Spline," CIRJE F-Series CIRJE-F-845, CIRJE, Faculty of Economics, University of Tokyo.
    9. Borus Jungbacker & Siem Jan Koopman, 2006. "Model-Based Measurement of Actual Volatility in High-Frequency Data," Advances in Econometrics, in: Econometric Analysis of Financial and Economic Time Series, pages 183-210, Emerald Group Publishing Limited.
    10. Charles Bos & Neil Shephard, 2006. "Inference for Adaptive Time Series Models: Stochastic Volatility and Conditionally Gaussian State Space Form," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 219-244.
    11. Patton, Andrew J. & Ziegel, Johanna F. & Chen, Rui, 2019. "Dynamic semiparametric models for expected shortfall (and Value-at-Risk)," Journal of Econometrics, Elsevier, vol. 211(2), pages 388-413.
    12. Gaglianone, Wagner Piazza & Guillén, Osmani Teixeira de Carvalho & Figueiredo, Francisco Marcos Rodrigues, 2018. "Estimating inflation persistence by quantile autoregression with quantile-specific unit roots," Economic Modelling, Elsevier, vol. 73(C), pages 407-430.
    13. Natalia Nolde & Johanna F. Ziegel, 2016. "Elicitability and backtesting: Perspectives for banking regulation," Papers 1608.05498, arXiv.org, revised Feb 2017.
    14. Siem Jan Koopman & Marius Ooms & Irma Hindrayanto, 2009. "Periodic Unobserved Cycles in Seasonal Time Series with an Application to US Unemployment," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(5), pages 683-713, October.
    15. Drew Creal & Siem Jan Koopman & André Lucas, 2008. "A General Framework for Observation Driven Time-Varying Parameter Models," Tinbergen Institute Discussion Papers 08-108/4, Tinbergen Institute.
    16. Siem Jan Koopman & Charles S. Bos, 2002. "Time Series Models with a Common Stochastic Variance for Analysing Economic Time Series," Tinbergen Institute Discussion Papers 02-113/4, Tinbergen Institute.
    17. Koopman, Siem Jan & Harvey, Andrew, 2003. "Computing observation weights for signal extraction and filtering," Journal of Economic Dynamics and Control, Elsevier, vol. 27(7), pages 1317-1333, May.
    18. Kum Hwa Oh & Eric Zivot & Drew Creal, 2006. "The Relationship between the Beveridge-Nelson Decomposition andUnobserved Component Models with Correlated Shocks," Working Papers UWEC-2006-16-FC, University of Washington, Department of Economics.
    19. Taylor, James W., 2021. "Evaluating quantile-bounded and expectile-bounded interval forecasts," International Journal of Forecasting, Elsevier, vol. 37(2), pages 800-811.
    20. Antonio Rubia Serrano & Lidia Sanchis-Marco, 2015. "Measuring Tail-Risk Cross-Country Exposures in the Banking Industry," Working Papers. Serie AD 2015-01, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).

    More about this item

    Keywords

    Asymmetric least squares Cubic splines Quantile regression Signal extraction State space smoother;

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:152:y:2009:i:2:p:179-185. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.