DPAL: A Test-Time Adaptation Loss for Financial Time Series Forecasting

Test-time adaptation (TTA) has recently emerged as a promising approach for improving time series forecasting (TSF) under distribution shift. Existing TSF-TTA methods differ in how they utilize revealed targets, yet the resulting adaptation protocols remain heterogeneous and lack a clearly unified formulation. To address this issue, we revisit TSF-TTA from the perspective of protocol cleanliness and propose an adaptation protocol based solely on matured ground truth, yielding a more principled setting for adaptation. Under this protocol, we further diagnose existing adapters in the frequency domain and find that their prediction corrections often exhibit limited and weakly structured spectral modifications. Motivated by this diagnosis, we propose Frequency-Aware Calibration (FAC), a lightweight calibration method that directly parameterizes prediction corrections in the frequency domain. Across diverse datasets, forecasting horizons, and source forecasters, FAC achieves competitive and consistent performance while requiring substantially fewer trainable parameters than the compared TSF-TTA adapters.

Test-time adaptation (TTA) methods for time-series forecasting update a deployed model, or a small adapter around it, from incoming ground truth. But the label of an $H$-step forecast exists only $H$ steps later, and real data pipelines add further delay. We build a leakage-free harness in which the label of forecast origin $s$ is released for updates only at step $s+d$ with $d \ge H$, and enforce this rule inside the released code of four recent TTA methods (TAFAS, COSA, PETSA and DynaTTA), run on their own backbones and checkpoints across five benchmarks (ETTm1, ETTh2, Weather, Electricity and Traffic). As references we add two closed-form correctors: a bank of recursive least squares (RLS) filters combined by a per-coordinate median, with no tunable hyperparameters and 56 microseconds per step on the 7-channel streams, and an ELF-style linear corrector. Under causal delayed labels the picture is asymmetric. On ETTm1 every audited method genuinely adapts, yet the RLS bank still beats three of the four at a fraction of their cost; only DynaTTA beats the bank, only at the minimum causal delay, and at roughly 2,500 times the per-update cost; the ELF-style corrector beats all four. On the other four datasets, the largest statistically significant improvement any published method achieves over its own frozen checkpoint is half a percent, on all four at least one published method is significantly worse than the frozen model at the minimum causal delay, and on drift-heavy ETTh2 longer label delays make every adapter that separates from the frozen model, ours included, significantly harmful. Leaky next-step updates inflate the apparent gains of simple adapters by up to 110%, and the backbone training recipe moves frozen online error by up to a factor of 25, more than any adaptation effect we measure. We release the harness, integration patches and all cached runs.

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 financial foundation models 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 improves adaptation over the pre-trained model, with the strongest gains under the primary evaluation (fore), driven primarily by reduced variance error. Overall, our results suggest that effective financial adaptation requires objectives that capture domain-specific temporal structure beyond token-level prediction.