March 2018

Spectral backtests of forecast distributions with application to risk management

Michael B. Gordy and Alexander J. McNeil


We study a class of backtests for forecast distributions in which the test statistic is a spectral transformation that weights exceedance events by a function of the modeled probability level. The choice of the kernel function 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 propose novel variants as well. 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.
Accessible materials (.zip)

Keywords: Backtesting, Risk management, Volatility


PDF: Full Paper

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Last Update: January 09, 2020