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We demonstrate that global tests do not perform well in this case because they were not designed to capture very short-lived instabilities, and their power vanishes altogether when the magnitude of the shock is very large. We then discuss non-parametric approaches that are more suitable to detect such situations. We illustrate these results in a Monte Carlo exercise and in a comparison of the nowcast of the quarterly US nominal GDP from the Survey of Professional Forecasters against a naive benchmark of no growth, over a period that includes the GDP instability brought by the COVID-19 crisis. 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