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Board of Governors of the Federal Reserve System (US)
Finance and Economics Discussion Series
Spectral Backtests of Forecast Distributions with Application to Risk Management
Michael B. Gordy
Alexander J. McNeil
Abstract

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.


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Michael B. Gordy & Alexander J. McNeil, Spectral Backtests of Forecast Distributions with Application to Risk Management, Board of Governors of the Federal Reserve System (US), Finance and Economics Discussion Series 2018-021, 23 Mar 2018.
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Keywords: Backtesting ; Risk management ; Volatility
DOI: 10.17016/FEDS.2018.021
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