Synth-FAR: A Synthetic Frequency-Autoregressive Driven Framework for Time Series Forecasting

Abstract: Time series forecasting is essential for predicting future values based on observed patterns. Traditional methods perform well in in-domain scenarios with ample data but struggle with scarce data, leading to the rise of zero-shot and few-shot learning. Recent advancements use large-scale models but require extensive data and resources, often learning ineffectively from the available data. This study explores factors influencing effective learning in time series forecasting using Fourier analysis. Findings show that forecasters struggle with data containing multiple frequencies and generalizing to unseen frequencies. To address this, we introduce Synth-FAR, a synthetic data generation framework that enhances or replaces real data by creating a mixture of autoregressive and frequency information, improving model robustness in limited data scenarios. Our method outperforms other popular synthetic data techniques, such as Kernel-Synth, in both generation time and performance, and demonstrates the potential for integration into foundation model data pipelines, thereby enhancing their effectiveness.

Submission Type: Regular submission (no more than 12 pages of main content)

Changes Since Last Submission:

**Submission**

* Added comparison to Chronos-bolt (Fig 3)
* Added comparison to TiRex (Fig 3)
* Added comparison to Sundial (Fig 3)

**Revision 28/04/2026**

* Updated and expanded Section **E.2 Full Experimental Results** (formerly section F.2) in the Appendix to include standard deviations for all main experiments, namely, Table 1, Table 2, and Figure 3. (viewer )

* Expanded the **Fourier analysis in time series applications** paragraph in the related work to include additional works on frequency-domain deep models, spectral bias, and spectral forecasting

* Revised Appendix Section **C.4: Synth-FAR Limitations** to explicitly address the requested failure cases and clarify scenarios where Synth-FAR is less effective.

* Moved the **Datasets and Models** section to the main paper to improve clarity and make the manuscript more self-contained.

* Emphasized connection to existing literature w.r.t frequency generalization/adaptation in section 4.1.

* Improved discussion in C.1 Fundamental Frequency Estimation.

**Revision 09/05/2026**

* Improved positioning and phrasing in the main text.

* Restructure of the related work section, including the paragraphs: **Frequency-domain learning models** and **Spectral learning and analysis**

Assigned Action Editor: ~Yunbo_Wang1

Submission Number: 7844