Handling Multi-Scale Seasonality in FFT-Based Downsampling

Investigate how to resolve ambiguity due to multi-scale seasonality (i.e., multiple significant spectral peaks) within the FFT-based downsampling procedure used by Reverso to select the dominant frequency and determine the downsampling stride, enabling reliable operation when more than one seasonal component is present.

Background

Reverso employs an FFT-based downsampling algorithm at inference time to bring seasonal patterns within the model’s fixed context window. The procedure detects a dominant frequency via spectral peak analysis and uses significance criteria to avoid spurious detections.

To reduce ambiguity, the method explicitly enforces the existence of a single dominant frequency, which prevents conflicts when multiple seasonalities coexist. The authors explicitly note that handling multi-scale seasonality (multiple strong spectral peaks) is left for future work, indicating an unresolved methodological gap.

Addressing this case would improve robustness in real-world time series where multiple seasonal components (e.g., daily and weekly cycles) can be present simultaneously, and would clarify how to select peaks and compute strides without relying on a single-frequency assumption.

References

Equation \ref{eq:peak_dominance} ensures a single dominant frequency exists, mitigating ambiguity from multi-scale seasonality which we leave for future work.

— Reverso: Efficient Time Series Foundation Models for Zero-shot Forecasting  (2602.17634 - Fu et al., 19 Feb 2026) in Appendix: Downsampling Algorithm