FTSformer brings multi-scale transformers to financial time series forecasting

Financial markets have long been regarded as one of the most hostile environments for forecasting algorithms. Prices swing violently, relationships between assets shift without warning, and the signals that truly drive an asset’s trajectory are often hidden in external forces rather than in its own past behavior. A newly published study in the International Journal of Machine Learning and Cybernetics tackles this challenge head-on with FTSformer, a financial-initiated multi-scale transformer framework that fuses exogenous information from both the time and frequency domains to deliver more accurate, more stable forecasts. The work, led by Zongxin Dong of the Frontier Interdisciplinary Domain at Beijing Institute Technology Zhuhai, together with Shuangshuang Li and Guangyuan Pan of Linyi University, Zhenghong Bi of Beijing Institute of Technology Zhuhai, and Chuanxia Hu of Inner Mongolia Medical University, demonstrates error reductions of up to 13.4 percent on the widely used Exchange benchmark and consistent gains over strong baseline models across multiple public datasets.

The core insight behind FTSformer is deceptively simple but technically demanding. Most existing forecasting architectures, including sophisticated transformer models that have dominated long-horizon time series benchmarks, concentrate almost exclusively on the historical behavior of the target variable. They learn the internal dynamics of a single asset and extrapolate from them. Yet financial time series are shaped by an intricate web of external drivers: macroeconomic indicators, sector indices, and cross-asset signals all exert latent coupling effects on the target. When these exogenous variables are ignored or treated as generic side inputs, models lose critical information about why a market moves, not merely how it moved. The researchers set out to build an architecture that simultaneously captures cross-asset interactions, multi-scale temporal dynamics, and the notoriously complex loss landscape that deep forecasting models must navigate.

At the heart of the framework lies the Dual-Domain Fusion Layer, or DDF, a module designed to extract and fuse heterogeneous exogenous information in both the time domain and the frequency domain. Time-domain features capture raw temporal patterns such as trends and sudden shocks, while frequency-domain representations expose periodicities and oscillatory components that are invisible in raw waveforms. By jointly processing both domains and explicitly emphasizing their intrinsic heterogeneity, the DDF layer allows the model to distinguish, for example, between a slow-moving macroeconomic drift and a fast, cyclical sector rotation that may both influence the same stock. This dual-domain strategy reflects a broader trend in modern time series research, where frequency-enhanced architectures such as FEDformer have shown that spectral information can substantially improve long-term forecasting, but extends it by systematically integrating external signals rather than only the target series.

Complementing the fusion layer, the researchers introduce a Multi-Scale Temporal Partition mechanism, abbreviated MSTP, together with a Channel-Modulation Preprocessor known as CMP. Financial data unfold at multiple characteristic timescales simultaneously: intraday noise, weekly rhythms, monthly cycles, and secular trends all coexist in a single price series. The MSTP mechanism partitions the input sequence across these scales so that the model can attend to short-lived fluctuations and long-range dependencies without forcing one convolutional or attention window to serve all purposes. The CMP, in turn, addresses a practical problem that plagues multivariate forecasting: different input channels arrive with vastly different signal strengths. A dominant channel can overwhelm weaker but informative ones during training, destabilizing gradients and slowing convergence. The CMP dynamically adapts the weights assigned to each input channel, balancing signal strengths before the core temporal modeling module ever sees the data. According to the authors, this preprocessing step measurably enhances both training stability and convergence speed, an advantage that becomes evident in the ablation experiments reported in the paper.

The temporal backbone of FTSformer is a component the authors call BA-LSTM, a bidirectional long short-term memory architecture tasked with capturing both short-term market fluctuations and long-term dependencies. LSTMs, first popularized in the deep learning era for sequence modeling, remain a powerful tool for financial prediction, and hybrid designs combining recurrent networks with transformers have proliferated in recent literature. In FTSformer, the BA-LSTM operates in concert with the transformer’s attention machinery, providing a recurrent pathway that preserves order-sensitive information while the attention layers model global interactions across the multi-scale, exogenously enriched representations. This division of labor echoes a recurring theme in the forecasting literature, where purely attention-based models sometimes struggle with the strong nonlinearity and regime changes characteristic of financial data.

The empirical evaluation is unusually broad for a methods paper in this domain. The team tested FTSformer on multiple public benchmark datasets as well as a real-world Canadian traffic dataset, deliberately stepping outside finance to probe cross-domain transferability. The headline result is a reduction in forecasting errors of up to 13.4 percent on the Exchange dataset, a benchmark notorious for its nonstationary exchange-rate dynamics that punish rigid models. Across the full suite of public benchmarks, the model achieved average reductions of 1.54 percent in root mean square error and 2.22 percent in mean absolute error over the strongest baseline. While single-digit average gains may appear modest, in competitive forecasting benchmarks where state-of-the-art models are separated by fractions of a percent, such improvements are meaningful, and the consistency of gains across heterogeneous datasets suggests the architecture captures something genuinely general rather than dataset-specific.

Equally notable are the results on training stability and robustness. The authors report that FTSformer substantially outperforms existing baselines not only in accuracy but also in the stability of its training process, an attribute they attribute to the Channel-Modulation Preprocessor’s balancing of channel signals before temporal modeling. They further evaluated robustness to exogenous perturbations, deliberately injecting noise or distortions into the external variables to simulate real-world conditions in which exogenous data sources may be incomplete, delayed, or corrupted. The model’s performance degraded more gracefully than that of competing methods, reinforcing the value of explicitly modeling the heterogeneity of external information rather than naively concatenating it into the input tensor. This robustness finding carries practical weight for financial institutions, where data pipelines are rarely pristine and a model that collapses when an indicator feed fails is of limited operational use.

The study situates itself within a rapidly evolving landscape of time series transformers. The original transformer architecture, introduced in 2017 for machine translation, was adapted to forecasting by models such as Informer and Autoformer, which introduced sparse attention and decomposition strategies for long sequences. More recently, iTransformer reoriented the attention mechanism across variables rather than time steps, while TimeXer explicitly empowered transformers with exogenous variables, a direct conceptual ancestor of FTSformer’s exogenous fusion philosophy. Meanwhile, finance-specific transformers such as Master have explored market-guided attention, and questions about whether transformers are even the right inductive bias for time series, posed pointedly by Zeng and colleagues in their DLinear work, continue to animate the field. FTSformer’s contribution is to combine the multi-scale decomposition trend with a principled, dual-domain treatment of exogenous heterogeneity, targeting the specific pathologies of financial data: high volatility, strong nonlinearity, and pronounced dependence on external drivers.

The authors are careful to frame the work as a flexible, exogenous-aware forecasting framework rather than a finance-only tool. The inclusion of the Canadian traffic dataset is a deliberate demonstration that the architecture’s benefits extend beyond markets, and the paper reports promising cross-domain transferability, suggesting that the dual-domain fusion and channel modulation principles could generalize to energy demand, weather, epidemiology, or any multivariate setting where external covariates drive the target. For practitioners in quantitative finance, the framework arrives amid growing interest in machine learning methods for asset pricing and risk management, following influential work such as Gu, Kelly, and Xiu’s empirical asset pricing study and the continuing proliferation of deep learning surveys in the field. The research was supported by the National Natural Science Foundation of China under Grant 62103177 and by the Key Technology Research and Development Program of Shandong Province under Grant 2025TSGCCZZB0893.

What makes the paper resonant beyond its benchmark numbers is its conceptual reframing of the forecasting problem. Rather than asking how best to extrapolate a single series, FTSformer treats prediction as an exercise in multi-source reasoning: the target’s own multi-scale history, the time-domain and frequency-domain signatures of external drivers, and the relative reliability of every input channel must all be weighed together, dynamically, at every forecasting step. As markets grow more interconnected and data feeds multiply, that framing is likely to influence how the next generation of forecasting systems is built. The study, received on 2 February 2026, accepted on 19 August 2026, and published on 30 August 2026, adds a technically detailed and empirically validated entry to that conversation, one that argues the future of accurate forecasting lies not in ever-larger single-series models but in architectures that know how to listen to the world around the signal.