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Interquantile Expectation Regression

Author

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  • 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
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    File URL: https://papers.tinbergen.nl/17034.pdf
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. 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.
    2. Timo Dimitriadis & Andrew J. Patton & Patrick W. Schmidt, 2019. "Testing Forecast Rationality for Measures of Central Tendency," Papers 1910.12545, arXiv.org, revised Jul 2024.
    3. 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.
    4. 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.
    5. 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).
    6. Sebastian Bayer & Timo Dimitriadis, 2018. "Regression Based Expected Shortfall Backtesting," Papers 1801.04112, arXiv.org, revised Sep 2019.
    7. Tobias Fissler & Johanna F. Ziegel, 2019. "Evaluating Range Value at Risk Forecasts," Papers 1902.04489, arXiv.org, revised Nov 2020.
    8. Timo Dimitriadis & Julie Schnaitmann, 2019. "Forecast Encompassing Tests for the Expected Shortfall," Papers 1908.04569, arXiv.org, revised Aug 2020.

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    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

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