TIFO: Time-Invariant Frequency Operator for Stationarity-Aware Representation Learning in Time Series
#TIFO#Time‑Invariant Frequency Operator#Stationarity‑Aware Representation#Non‑Stationary Time Series#Distribution Shift#Fourier Transform#Eigen‑Decomposition#ETTm2 Dataset#Mean Squared Error#Plug‑and‑Play Module#Forecasting Models
📌 Key Takeaways
TIFO learns stationarity‑aware weights over the frequency spectrum from the entire dataset.
Addressing distribution shift in non‑stationary time‑series forecasting by modeling time‑evolving structure in frequency space.
Plug‑and‑play design that can be integrated into existing forecasting models.
Achieves top‑1 ranking in 18 out of 28 settings and top‑2 in 6 settings on benchmark tasks.
Improves average MSE by 33.3 % and 55.3 % on the ETTm2 dataset and reduces computational cost by 60 %‑70 %.
📖 Full Retelling
The researchers, led by Xihao Piao, introduce the Time‑Invariant Frequency Operator (TIFO), a new approach for stationarity‑aware representation learning in time‑series forecasting. They published the work on arXiv on 19 February 2026, targeting non‑stationary data that suffers from distribution shift between training and test sets. The paper proposes learning frequency‑dependent weights across the entire dataset to highlight stationary components while suppressing non‑stationary ones, thereby mitigating the shift and improving forecast accuracy.
TIFO treats the Fourier transform of a time series as an implicit eigen‑decomposition in frequency space, enabling a plug‑and‑play module that can be incorporated into various forecasting models. In experiments, TIFO tops 18 out of 28 forecasting settings and achieves 33.3 % and 55.3 % mean‑squared‑error improvements on the ETTm2 dataset. Additionally, it cuts computational costs by 60 %‑70 % compared to baseline methods, demonstrating strong scalability.
🏷️ Themes
Time‑Series Forecasting, Frequency Domain Analysis, Stationarity vs. Non‑Stationarity, Distribution Shift Mitigation, Representation Learning, Computational Efficiency
Entity Intersection Graph
No entity connections available yet for this article.
Deep Analysis
Why It Matters
TIFO tackles the distribution shift problem that plagues nonstationary time series forecasting by learning weights that emphasize stationary frequency components, leading to better accuracy and lower computational cost.
Context & Background
Nonstationary time series forecasting suffers from distribution shift between training and test data.
Existing methods that remove low-order moments fail to capture evolving time structures across samples.
TIFO operates in the frequency domain to highlight stationary components and suppress nonstationary ones.
What Happens Next
The TIFO operator is expected to be adopted by a wider range of forecasting models and may spur further research into frequency‑space techniques for time‑series analysis.
Frequently Asked Questions
What is TIFO?
TIFO is a plug‑and‑play operator that assigns weights to frequency components to reduce distribution shift in time series forecasting.
How does TIFO improve performance?
By focusing on stationary frequencies, TIFO reduces forecasting error and cuts computational costs by 60% to 70% compared to baseline methods.
Original Source
--> Computer Science > Machine Learning arXiv:2602.17122 [Submitted on 19 Feb 2026] Title: TIFO: Time-Invariant Frequency Operator for Stationarity-Aware Representation Learning in Time Series Authors: Xihao Piao , Zheng Chen , Lingwei Zhu , Yushun Dong , Yasuko Matsubara , Yasushi Sakurai View a PDF of the paper titled TIFO: Time-Invariant Frequency Operator for Stationarity-Aware Representation Learning in Time Series, by Xihao Piao and 5 other authors View PDF HTML Abstract: Nonstationary time series forecasting suffers from the distribution shift issue due to the different distributions that produce the training and test data. Existing methods attempt to alleviate the dependence by, e.g., removing low-order moments from each individual sample. These solutions fail to capture the underlying time-evolving structure across samples and do not model the complex time structure. In this paper, we aim to address the distribution shift in the frequency space by considering all possible time structures. To this end, we propose a Time-Invariant Frequency Operator , which learns stationarity-aware weights over the frequency spectrum across the entire dataset. The weight representation highlights stationary frequency components while suppressing non-stationary ones, thereby mitigating the distribution shift issue in time series. To justify our method, we show that the Fourier transform of time series data implicitly induces eigen-decomposition in the frequency space. TIFO is a plug-and-play approach that can be seamlessly integrated into various forecasting models. Experiments demonstrate our method achieves 18 top-1 and 6 top-2 results out of 28 forecasting settings. Notably, it yields 33.3% and 55.3% improvements in average MSE on the ETTm2 dataset. In addition, TIFO reduces computational costs by 60% -70% compared to baseline methods, demonstrating strong scalability across diverse forecasting models. Subjects: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI) Ci...
