IDEAS home Printed from https://ideas.repec.org/p/tin/wpaper/20170034.html
   My bibliography  Save this paper

Interquantile Expectation Regression

Author

Listed:
  • Sander Barendse

    (Erasmus University Rotterdam, The Netherlands)

Abstract

We propose a semiparametric estimator to determine the effects of explanatory variables on the conditional interquantile expectation (IQE) of the random variable of interest, without specifying the conditional distribution of the underlying random variables. IQE is the expected value of the random variable of interest given that its realization lies in an interval between two quantiles, or in an interval that covers the range of the distribution to the left or right of a quantile. Our so-called interquantile expectation regression (IQER) estimator is based on the GMM framework. We derive consistency and the asymptotic distribution of the estimator, and provide a consistent estimator of the asymptotic covariance matrix. Our results apply to stationary and ergodic time series. In a simulation study we show that our asymptotic theory provides an accurate approximation in small samples. We provide an empirical illustration in finance, in which we use the IQER estimator to estimate one-step-ahead daily expected shortfall conditional on previously observed daily, weekly, and monthly aggregated realized measures.

Suggested Citation

  • Sander Barendse, 2017. "Interquantile Expectation Regression," Tinbergen Institute Discussion Papers 17-034/III, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20170034
    as

    Download full text from publisher

    File URL: https://papers.tinbergen.nl/17034.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Giacomini, Raffaella & Komunjer, Ivana, 2005. "Evaluation and Combination of Conditional Quantile Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 416-431, October.
    2. James W. Taylor, 2008. "Using Exponentially Weighted Quantile Regression to Estimate Value at Risk and Expected Shortfall," Journal of Financial Econometrics, Oxford University Press, vol. 6(3), pages 382-406, Summer.
    3. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
    4. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    5. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, January.
    6. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 7(2), pages 174-196, Spring.
    7. Hansen, Bruce E., 1996. "Stochastic Equicontinuity for Unbounded Dependent Heterogeneous Arrays," Econometric Theory, Cambridge University Press, vol. 12(2), pages 347-359, June.
    8. Bai, Xuezheng & Russell, Jeffrey R. & Tiao, George C., 2003. "Kurtosis of GARCH and stochastic volatility models with non-normal innovations," Journal of Econometrics, Elsevier, vol. 114(2), pages 349-360, June.
    9. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    10. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    11. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    12. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    13. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
    14. Saralees Nadarajah & Bo Zhang & Stephen Chan, 2014. "Estimation methods for expected shortfall," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 271-291, February.
    15. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    16. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    17. James W. Taylor, 2008. "Estimating Value at Risk and Expected Shortfall Using Expectiles," Journal of Financial Econometrics, Oxford University Press, vol. 6(2), pages 231-252, Spring.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sander Barendse & Erik Kole & Dick van Dijk, 2023. "Backtesting Value-at-Risk and Expected Shortfall in the Presence of Estimation Error," Journal of Financial Econometrics, Oxford University Press, vol. 21(2), pages 528-568.
    2. Sebastian Bayer & Timo Dimitriadis, 2018. "Regression Based Expected Shortfall Backtesting," Papers 1801.04112, arXiv.org, revised Sep 2019.
    3. Tobias Fissler & Johanna F. Ziegel, 2019. "Evaluating Range Value at Risk Forecasts," Papers 1902.04489, arXiv.org, revised Nov 2020.
    4. 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.
    5. Timo Dimitriadis & Andrew J. Patton & Patrick W. Schmidt, 2019. "Testing Forecast Rationality for Measures of Central Tendency," Papers 1910.12545, arXiv.org, revised Jun 2023.
    6. Caporale, Guglielmo Maria & Zekokh, Timur, 2019. "Modelling volatility of cryptocurrencies using Markov-Switching GARCH models," Research in International Business and Finance, Elsevier, vol. 48(C), pages 143-155.
    7. Timo Dimitriadis & Julie Schnaitmann, 2019. "Forecast Encompassing Tests for the Expected Shortfall," Papers 1908.04569, arXiv.org, revised Aug 2020.
    8. Müller, Fernanda Maria & Santos, Samuel Solgon & Gössling, Thalles Weber & Righi, Marcelo Brutti, 2022. "Comparison of risk forecasts for cryptocurrencies: A focus on Range Value at Risk," Finance Research Letters, Elsevier, vol. 48(C).

    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. Yuru Sun & Worapree Maneesoonthorn & Ruben Loaiza-Maya & Gael M. Martin, 2023. "Optimal probabilistic forecasts for risk management," Papers 2303.01651, arXiv.org.
    2. David Happersberger & Harald Lohre & Ingmar Nolte, 2020. "Estimating portfolio risk for tail risk protection strategies," European Financial Management, European Financial Management Association, vol. 26(4), pages 1107-1146, September.
    3. 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.
    4. Taylor, James W., 2020. "Forecast combinations for value at risk and expected shortfall," International Journal of Forecasting, Elsevier, vol. 36(2), pages 428-441.
    5. James Ming Chen, 2018. "On Exactitude in Financial Regulation: Value-at-Risk, Expected Shortfall, and Expectiles," Risks, MDPI, vol. 6(2), pages 1-28, June.
    6. Haugom, Erik & Ray, Rina & Ullrich, Carl J. & Veka, Steinar & Westgaard, Sjur, 2016. "A parsimonious quantile regression model to forecast day-ahead value-at-risk," Finance Research Letters, Elsevier, vol. 16(C), pages 196-207.
    7. Werner Ehm & Tilmann Gneiting & Alexander Jordan & Fabian Krüger, 2016. "Of quantiles and expectiles: consistent scoring functions, Choquet representations and forecast rankings," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 505-562, June.
    8. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    9. Vica Tendenan & Richard Gerlach & Chao Wang, 2020. "Tail risk forecasting using Bayesian realized EGARCH models," Papers 2008.05147, arXiv.org, revised Aug 2020.
    10. Eliana Christou & Michael Grabchak, 2022. "Estimation of Expected Shortfall Using Quantile Regression: A Comparison Study," Computational Economics, Springer;Society for Computational Economics, vol. 60(2), pages 725-753, August.
    11. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    12. Dimitriadis, Timo & Schnaitmann, Julie, 2021. "Forecast encompassing tests for the expected shortfall," International Journal of Forecasting, Elsevier, vol. 37(2), pages 604-621.
    13. Pfarrhofer, Michael, 2022. "Modeling tail risks of inflation using unobserved component quantile regressions," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    14. 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.
    15. Ewa Ratuszny, 2015. "Risk Modeling of Commodities using CAViaR Models, the Encompassing Method and the Combined Forecasts," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 15, pages 129-156.
    16. Le, Trung H., 2020. "Forecasting value at risk and expected shortfall with mixed data sampling," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1362-1379.
    17. Edgars Jakobsons & Steven Vanduffel, 2015. "Dependence Uncertainty Bounds for the Expectile of a Portfolio," Risks, MDPI, vol. 3(4), pages 1-25, December.
    18. Tadese, Mekonnen & Drapeau, Samuel, 2020. "Relative bound and asymptotic comparison of expectile with respect to expected shortfall," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 387-399.
    19. Daouia, Abdelaati & Padoan, Simone A. & Stupfler, Gilles, 2023. "Extreme expectile estimation for short-tailed data, with an application to market risk assessment," TSE Working Papers 23-1414, Toulouse School of Economics (TSE).
    20. Tobias Fissler & Jana Hlavinová & Birgit Rudloff, 2021. "Elicitability and identifiability of set-valued measures of systemic risk," Finance and Stochastics, Springer, vol. 25(1), pages 133-165, January.

    More about this item

    Keywords

    quantile; interquantile expectation; regression; generalized method of moments; risk management; expected shortfall;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:tin:wpaper:20170034. 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: Tinbergen Office +31 (0)10-4088900 (email available below). General contact details of provider: https://edirc.repec.org/data/tinbenl.html .

    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.