Forgetting and Tail Instability in Adaptive Volatility Forecasting

Abstract

Continual learning requires a choice about how quickly old information should lose influence. This paper studies the tail-risk consequences of that choice in adaptive volatility forecasting. Using daily historical replay for four equity markets, I estimate a recursive HAR-type forecasting architecture with forgetting factors from 1.0000 to 0.9950, holding the model and information set fixed while varying only the rate at which past observations are discounted. Point estimates for mild forgetting are sometimes favorable after stress onsets, but event-level confidence intervals include zero; no general relearning benefit is established. The robust result is instead a nonlinear tail cost. Using each market’s no-forgetting 99th-percentile QLIKE as a fixed descriptive catastrophic-failure threshold, the full-sample failure rate rises from about 1.03% with no forgetting to 2.03% at λ=0.995. A market-fixed-effect logit estimates a positive full-sample forgetting gradient (coefficient 0.0129 per basis point of 1−λ, p=0.001). A prospective threshold exercise preserves the direction but yields a smaller endpoint increase, from 1.40% to 1.80%, so the magnitude is threshold-construction sensitive. Aggressive forgetting also lengthens failure episodes in the primary classification, although bootstrap uncertainty and the prospective-duration check do not independently resolve persistence. Stress-window amplification is economically large in some markets but not precisely estimated as a universal interaction. A transparent 10/22/44-day HAR-RLS horizon check retains a pooled tail-failure penalty at aggressive forgetting, while also showing market-horizon heterogeneity. The paper therefore characterizes a market-dependent adaptationinstability region rather than a universal critical forgetting factor.

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