Volatility-Clustering Adaptation for Financial Time Series

Time-series foundation models are increasingly adapted to new domains through fine-tuning on target data, under the implicit assumption that more target data yields better forecasts. We show that this assumption can fail in financial forecasting, where individual price changes are difficult to predict, but large moves tend to cluster, creating alternating calm and turbulent periods. Using Kronos, a foundation model trained on price bars of open, high, low, close, and volume, we argue that adapting to financial domains requires training signals beyond next-token prediction. We introduce **Volatility-Clustering Adaptation (VCA)**, which augments next-token cross-entropy with a differentiable penalty on the autocorrelation of squared returns, the standard statistical signature of volatility clustering. This additional objective provides a multi-step training signal by matching the resulting dependence structure of autoregressive rollouts to those of the realized future. Across three asset sets and two evaluation conventions, VCA delivers the best average performance and highest win rate against the pre-trained model without fine-tuning, typically improving RankIC at some cost in ${\sigma }^2$-MAE. Overall, our results suggest that effective financial adaptation may require objectives that capture domain-specific temporal structure beyond token-level prediction.