A Rare-Disaster Wavelet State: Multiscale Disaster Regimes with a Certification Boundary

Why can a rare economic disaster explain the large reward investors demand for holding stocks, yet leave us unable to say how likely that disaster is or how bad it would be? This paper separates what the data can and cannot recover inside the disaster channel. Using a scale-by-scale wavelet decomposition of stock returns, it recovers the long-memory of returns, a classifier that marks calm versus turbulent regimes, and a law linking memory to volatility across scales. It shows the disaster's probability and size are not separately recoverable: many very different pairs match the same premium, their product varying almost sixteenfold. A pre-registered test shows the disaster signal forecasts volatility, not returns. It dates regimes; it does not lead them.