Battling the Non-stationarity in Time Series Forecasting via Test-time Adaptation

TL;DR

Non-stationarity degrades pre-trained time series forecasters, motivating test-time adaptation for TSF (TSF-TTA). The paper introduces TAFAS, a model-agnostic framework that uses periodicity-aware adaptation scheduling (PAAS) to obtain semantically meaningful partially-observed ground truth and a gated calibration module (GCM) to locally and globally calibrate inputs and outputs, while keeping the original forecaster frozen. The approach combines partial and full adaptation losses, enabling proactive adjustment of future predictions without overwriting learned temporal semantics, and demonstrates substantial gains across seven datasets, multiple architectures, and even foundation models (Chronos), especially for long-horizon forecasting (up to ~45% improvement in some settings). These results highlight TAFAS’s potential for robust, scalable deployment of TSF models in non-stationary environments, and its compatibility with pre-training-based non-stationarity remedies and large-time-series foundation models.

Abstract

Deep Neural Networks have spearheaded remarkable advancements in time series forecasting (TSF), one of the major tasks in time series modeling. Nonetheless, the non-stationarity of time series undermines the reliability of pre-trained source time series forecasters in mission-critical deployment settings. In this study, we introduce a pioneering test-time adaptation framework tailored for TSF (TSF-TTA). TAFAS, the proposed approach to TSF-TTA, flexibly adapts source forecasters to continuously shifting test distributions while preserving the core semantic information learned during pre-training. The novel utilization of partially-observed ground truth and gated calibration module enables proactive, robust, and model-agnostic adaptation of source forecasters. Experiments on diverse benchmark datasets and cutting-edge architectures demonstrate the efficacy and generality of TAFAS, especially in long-term forecasting scenarios that suffer from significant distribution shifts. The code is available at https://github.com/kimanki/TAFAS.

Figures (6)

• Figure 1: (a) The performance of a pre-trained source forecaster degrades when it encounters distribution-shifted inputs at test-time. In the figure, the distribution shift occurs through the gradual increase of mean value. (b) The sequential nature of time series provides the opportunity to proactively adapt the forecaster with partially-observed ground truth (POGT) before acquiring full ground truth (GT).
• Figure 2: An overview of TAFAS. (1: Blue) By computing the periodicity of dominant patterns for $\bm{X}_{t^*}$, PAAS determines the length of partially-observed ground truth (POGT) $p_{t^*}$. (2: Yellow) Then input and output GCMs are proactively adapted on $\bm{X}_{t^*}$ at $t^* + p_{t^*}$ to mitigate local and global distribution shifts through Temporal Calibration (TC) and gating (tanh) mechanisms, by minimizing MSE between the POGT and corresponding prediction. The source forecaster is frozen to preserve its core semantic information learned. (3: Green) Following the proactive adaptation, predictions for test mini-batch $\{\bm{X}\}_{t^*}^{t^* + p_{t^*}}$ are recalculated to reflect the distribution shift and the unobserved part of the original predictions is adjusted with the adapted predictions.
• Figure 3: Comparison of PAAS against using a fixed POGT length on the ETTh1 dataset.
• Figure A1: Improvements of MSE (%) as the forecasting window length increases.
• Figure A2: Visualization of forecasting results with and without TAFAS. The top row illustrates that TAFAS effectively adapts to both low-frequency (top left) and high-frequency (top right) dominant patterns within the look-back window. The bottom row highlights the promising aspect of TAFAS in significantly more challenging scenarios characterized by pronounced global distribution shifts.