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A consistent specification test for dynamic quantile models

Author

Listed:
  • Peter Horvath
  • Jia Li
  • Zhipeng Liao
  • Andrew J. Patton
Abstract
Correct specification of a conditional quantile model implies that a particular conditional moment is equal to zero. We nonparametrically estimate the conditional moment function via series regression and test whether it is identically zero using uniform functional inference. Our approach is theoretically justified via a strong Gaussian approximation for statistics of growing dimensions in a general time series setting. We propose a novel bootstrap method in this nonstandard context and show that it significantly outperforms the benchmark asymptotic approximation in finite samples, especially for tail quantiles such as Value‐at‐Risk (VaR). We use the proposed new test to study the VaR and CoVaR (Adrian and Brunnermeier (2016)) of a collection of US financial institutions.

Suggested Citation

  • Peter Horvath & Jia Li & Zhipeng Liao & Andrew J. Patton, 2022. "A consistent specification test for dynamic quantile models," Quantitative Economics, Econometric Society, vol. 13(1), pages 125-151, January.
    • Handle: RePEc:wly:quante:v:13:y:2022:i:1:p:125-151
    DOI: 10.3982/QE1727
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    References listed on IDEAS

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    Cited by:

    1. Corradi, Valentina & Fosten, Jack & Gutknecht, Daniel, 2023. "Out-of-sample tests for conditional quantile coverage an application to Growth-at-Risk," Journal of Econometrics, Elsevier, vol. 236(2).
    2. Sullivan Hu'e & Christophe Hurlin & Yang Lu, 2024. "Backtesting Expected Shortfall: Accounting for both duration and severity with bivariate orthogonal polynomials," Papers 2405.02012, arXiv.org, revised May 2024.
    3. Christis Katsouris, 2023. "Quantile Time Series Regression Models Revisited," Papers 2308.06617, arXiv.org, revised Aug 2023.

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