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Spectral backtests of forecast distributions with application to risk management

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  • Michael B. Gordy
  • Alexander J. McNeil

Abstract

We study a class of backtests for forecast distributions in which the test statistic depends on a spectral transformation that weights exceedance events by a function of the modeled probability level. The weighting scheme is specified by a kernel measure which makes explicit the user's priorities for model performance. The class of spectral backtests includes tests of unconditional coverage and tests of conditional coverage. We show how the class embeds a wide variety of backtests in the existing literature, and further propose novel variants which are easily implemented, well-sized and have good power. In an empirical application, we backtest forecast distributions for the overnight P&L of ten bank trading portfolios. For some portfolios, test results depend materially on the choice of kernel.

Suggested Citation

  • Michael B. Gordy & Alexander J. McNeil, 2017. "Spectral backtests of forecast distributions with application to risk management," Papers 1708.01489, arXiv.org, revised Jul 2019.
    • Handle: RePEc:arx:papers:1708.01489
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    Cited by:

    1. Alexander J. McNeil, 2020. "Modelling volatile time series with v-transforms and copulas," Papers 2002.10135, arXiv.org, revised Jan 2021.
    2. Orla Mccullagh & Mark Cummins & Sheila Killian, 2023. "The Fundamental Review of the Trading Book: Implications for Portfolio and Risk Management in the Banking Sector," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 55(7), pages 1785-1816, October.
    3. 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.
    4. Nick Costanzino & Michael Curran, 2018. "A Simple Traffic Light Approach to Backtesting Expected Shortfall," Risks, MDPI, vol. 6(1), pages 1-7, January.
    5. Soren Bettels & Sojung Kim & Stefan Weber, 2022. "Multinomial Backtesting of Distortion Risk Measures," Papers 2201.06319, arXiv.org, revised Aug 2024.

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    More about this item

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation
    • 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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