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Dynamic testing of volatility models’ calibration using E-values

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  • Di Leonforte, Davide Carmelo
  • Deliu, Nina

Abstract

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.

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  • Di Leonforte, Davide Carmelo & Deliu, Nina, 2025. "Dynamic testing of volatility models’ calibration using E-values," Statistics & Probability Letters, Elsevier, vol. 226(C).
    • Handle: RePEc:eee:stapro:v:226:y:2025:i:c:s0167715225001609
    DOI: 10.1016/j.spl.2025.110515
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