Dynamic testing of volatility models’ calibration using E-values

We propose a novel framework for dynamic model choice in financial volatility forecasting using e-values. E-values provide a valid, yet flexible statistical framework for sequential testing, making them particularly suitable for testing model adequacy in real-time settings. Focusing on the probabilistic calibration of GARCH volatility models, we show empirically how e-values can effectively identify if and when a volatility model is or becomes miscalibrated. Finally, we present new insights on the why, after inspecting the realised e-process and its relationship with the historical returns of the Apple asset. In particular, we believe that e-values may be regarded as an early warning tool of market instability (linking it to the leverage effect and market asymmetries) and as early predictors of high-volatility clusters.