Spectral backtests of forecast distributions with application to risk management

Alexander John McNeil, Michael Gordy

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Article number105817
Number of pages13
JournalJournal of Banking and Finance
Early online date16 May 2020
Publication statusPublished - Jul 2020

Bibliographical note

© Elsevier, 2020. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy.


  • Backtesting; Volatility; Risk management

Cite this