Test-Time Adaptation for Non-stationary Time Series: From Synthetic Regime Shifts to Financial Markets

TL;DR

Non-stationary time series degrade performance when deployed models face distribution shifts. The authors propose a small-footprint test-time adaptation framework that freezes the backbone and updates only normalization affine parameters $$(\gamma,\beta)$$ using unlabeled recent windows, complemented by entropy/consistency objectives for classification and variance/EMA-teacher losses for regression, plus a drift penalty and uncertainty-based fallback. Evaluation across synthetic regime shifts on ETTh datasets and real-market data (SPY, QQQ, EUR/USD) reveals that batch-normalization statistics refresh is a robust default in financial series, while norm-only updates help in smooth drift scenarios; combining these with a cautious uncertainty trigger yields safer, more effective adaptation. Econometric tests (Diebold--Mariano) and Newey--West backtests corroborate gains in regime-aware contexts, offering practical guidelines for deploying TTA in streaming non-stationary time series. The work advances a practical, explainable pathway for TTA, highlighting when small-footprint adaptation helps or hurts and how to monitor and safeguard performance in real-time deployments.

Abstract

Time series encountered in practice are rarely stationary. When the data distribution changes, a forecasting model trained on past observations can lose accuracy. We study a small-footprint test-time adaptation (TTA) framework for causal timeseries forecasting and direction classification. The backbone is frozen, and only normalization affine parameters are updated using recent unlabeled windows. For classification we minimize entropy and enforce temporal consistency; for regression we minimize prediction variance across weak time-preserving augmentations and optionally distill from an EMA teacher. A quadratic drift penalty and an uncertainty triggered fallback keep updates stable. We evaluate this framework in two stages: synthetic regime shifts on ETT benchmarks, and daily equity and FX series (SPY, QQQ, EUR/USD) across pandemic, high-inflation, and recovery regimes. On synthetic gradual drift, normalization-based TTA improves forecasting error, while in financial markets a simple batch-normalization statistics update is a robust default and more aggressive norm-only adaptation can even hurt. Our results provide practical guidance for deploying TTA on non-stationary time series.

Figures (3)

• Figure 1: Regime diagnostics for SPY volatility and returns.
• Figure 2: Rolling forecast metrics on ETTh1 under gradual drift.
• Figure 3: Rolling metrics for SPY, QQQ, and EUR/USD with regime shading.