Beyond Forecasts: Refining Foundation Models for Smarter Financial Predictions

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Author: Denis Avetisyan

A new approach, RefineBridge, significantly boosts the accuracy of financial time series forecasting by intelligently refining the outputs of powerful foundation models.

RefineBridge employs a Schrödinger Bridge to learn an optimal transport map, progressively refining initial forecasts along sampling steps to more closely align with ground truth, acknowledging that all predictive systems inevitably drift from perfect accuracy with the passage of time.
RefineBridge employs a Schrödinger Bridge to learn an optimal transport map, progressively refining initial forecasts along sampling steps to more closely align with ground truth, acknowledging that all predictive systems inevitably drift from perfect accuracy with the passage of time.

RefineBridge leverages Schrödinger Bridge optimal transport to improve probabilistic forecasts from Time Series Foundation Models, outperforming methods like Low-Rank Adaptation.

Financial time series forecasting remains a formidable challenge for even the most advanced transformer-based foundation models due to inherent data complexities like non-stationarity and noise. This paper introduces RefineBridge: Generative Bridge Models Improve Financial Forecasting by Foundation Models, a novel post-processing module designed to enhance these models’ predictive accuracy. By leveraging a tractable Schrödinger Bridge framework for optimal transport, RefineBridge learns to refine initial forecasts, iteratively aligning them with ground truth data and consistently outperforming methods like LoRA across multiple benchmarks. Could this approach unlock more robust and reliable financial forecasting capabilities, paving the way for improved investment strategies and risk management?

The Inherent Instability of Financial Echoes

Financial time series present a unique forecasting challenge due to their inherent statistical complexities. Unlike many other datasets, financial data frequently demonstrates non-stationarity – meaning its statistical properties, such as mean and variance, change over time, invalidating assumptions of traditional forecasting methods. Furthermore, \text{heteroskedasticity} – the varying volatility often observed in financial markets – introduces uneven error distributions, impacting the reliability of predictions. These characteristics mean that models designed for stable data often falter when applied to financial instruments, necessitating specialized techniques capable of adapting to shifting market dynamics and accurately assessing risk associated with fluctuating price movements. Consequently, achieving consistently accurate forecasts in finance requires a deep understanding of these non-stationary and heteroskedastic properties, and the implementation of robust modeling strategies to mitigate their effects.

Conventional time series analyses, such as simple moving averages or autoregressive models, frequently encounter limitations when applied to financial data. These methods often assume stationary data – a constant mean and variance over time – a condition rarely met in financial markets exhibiting trends, seasonality, and volatility clustering. Consequently, they struggle to model the dynamic relationships and intricate dependencies present in financial time series. Furthermore, linear models may fail to capture the non-linear patterns and regime shifts common in asset prices, leading to inaccurate forecasts and potentially significant financial risk. The inability to adapt to changing market conditions and fully exploit the information contained within historical data underscores the need for more sophisticated approaches capable of handling the inherent complexities of financial time series.

Financial time series data fundamentally rely on autocorrelation – the degree to which past values influence future ones – necessitating modeling approaches that skillfully capture these historical dependencies. Unlike purely random processes, financial data exhibit discernible patterns where trends and cycles persist, though often obscured by noise and volatility. Effective forecasting, therefore, isn’t simply about predicting the next random event; it’s about identifying and quantifying these lagged relationships. Models that ignore this inherent autocorrelation, such as those assuming complete independence between data points, consistently underperform. Instead, techniques like autoregressive integrated moving average (ARIMA) models, and increasingly, sophisticated machine learning algorithms designed to recognize temporal patterns, aim to extrapolate future values by learning from the series’ own past behavior, effectively turning historical data into a predictive asset. The strength of these models lies in their capacity to weigh recent patterns more heavily, adapt to changing market dynamics, and ultimately, provide more robust and accurate predictions than methods that treat each data point in isolation.

Foundation Models: A Shift in Temporal Understanding

Time Series Foundation Models (TSFMs) signify a move away from traditional, task-specific time series modeling approaches. Prior methods typically required training models from scratch for each new dataset or forecasting problem. TSFMs, however, are pre-trained on extensive, unlabeled time series data-often exceeding the scale of datasets used in prior research-to learn general temporal patterns and representations. This pre-training process allows the models to then be adapted to downstream tasks with significantly less labeled data and computational resources than would be required for training from scratch. The core principle is that the pre-trained model has already acquired a broad understanding of time series dynamics, enabling faster convergence and improved performance on a variety of forecasting, classification, and anomaly detection problems.

Time Series Foundation Models (TSFMs) like Chronos, Moirai, and Time-MoE are built upon the Transformer architecture, originally developed for natural language processing. This architecture employs self-attention mechanisms which allow the model to weigh the importance of different time steps in a series when making predictions, effectively capturing long-range temporal dependencies. Unlike recurrent neural networks (RNNs) which process data sequentially, Transformers can process the entire time series in parallel, improving computational efficiency. The self-attention mechanism calculates relationships between all pairs of time steps, enabling the model to identify patterns and correlations that might be missed by models with limited receptive fields. These models utilize multi-head attention to further enhance the representation of temporal dependencies by learning multiple attention patterns simultaneously.

Parameter-efficient fine-tuning (PEFT) methods, such as Low-Rank Adaptation (LoRA), address the computational cost of adapting large Time Series Foundation Models (TSFMs) to downstream tasks. LoRA freezes the pre-trained model weights and introduces trainable low-rank decomposition matrices into each layer of the Transformer architecture. This significantly reduces the number of trainable parameters – often by over 90% – compared to full fine-tuning, while maintaining comparable performance. By only updating these smaller matrices, LoRA minimizes computational requirements and storage costs, facilitating efficient adaptation to diverse time series datasets and tasks without incurring the expense of training all model parameters. Other PEFT methods include adapters and prefix tuning, each offering different trade-offs between parameter efficiency and performance.

RefineBridge enhances the accuracy of Transformer-based State Forecasting Models (TSFMs) by iteratively refining their predictions-conditioned on contextual information-using either Stochastic Differential Equations (SDE) or Ordinary Differential Equations (ODE) sampling, as demonstrated by the improved prediction in the example shown.
RefineBridge enhances the accuracy of Transformer-based State Forecasting Models (TSFMs) by iteratively refining their predictions-conditioned on contextual information-using either Stochastic Differential Equations (SDE) or Ordinary Differential Equations (ODE) sampling, as demonstrated by the improved prediction in the example shown.

RefineBridge: Guiding Predictions Towards Reality

RefineBridge improves Time Series Forecasting Model (TSFM) performance through a refinement process utilizing Schrödinger Bridges. This approach treats the initial TSFM prediction as a probability distribution and aims to transform it into a more accurate distribution reflecting observed data. The Schrödinger Bridge constructs a diffusion process connecting these two distributions, effectively guiding the initial prediction towards the target distribution defined by the actual observations. This differs from traditional post-processing methods by providing a theoretically grounded framework for iterative refinement, minimizing the divergence between predicted and observed time series data. The method allows for incorporating observational information directly into the prediction refinement, addressing limitations of purely data-driven or statistical post-correction techniques.

The RefineBridge paradigm utilizes Optimal Transport (OT) to refine time series forecasting models by transforming probability distributions. Initial predictions are treated as a source distribution, and the observed data represents the target distribution. OT calculates a transport plan – a mapping – that minimizes the cost of moving probability mass from the initial prediction to align with the observed data. This process effectively adjusts the predicted distribution, bringing it closer to the empirical distribution of actual values. The cost function, typically based on a distance metric like the Wasserstein distance \W(P,Q), quantifies the dissimilarity between the two distributions, and its minimization provides a principled way to refine the forecast by leveraging information contained within the observed data.

The RefineBridge architecture utilizes a decomposition stage employing DLinear to separate time series data into trend and seasonality components. This decomposition facilitates more accurate refinement by isolating underlying patterns. Subsequently, a 1D U-Net is implemented as a denoiser, processing the decomposed time series and initial predictions to reduce residual errors and improve prediction fidelity. The U-Net’s architecture, characterized by an encoder-decoder structure with skip connections, allows for the preservation of fine-grained details during the denoising process, ultimately contributing to enhanced overall prediction quality.

Assessing Resilience and Forecasting Prowess

Financial time series are notoriously susceptible to outliers – extreme values resulting from unexpected events or market volatility – which can severely distort model training and prediction accuracy. Robust normalization techniques address this challenge by rescaling the data in a way that minimizes the influence of these anomalous points. Unlike standard normalization methods that are sensitive to outliers, robust approaches – such as using medians and interquartile ranges instead of means and standard deviations – provide a more stable and reliable foundation for forecasting models. This preprocessing step is therefore critical, not only for improving predictive performance but also for ensuring the overall stability and trustworthiness of financial models operating in dynamic and often unpredictable markets. By mitigating the impact of extreme values, robust normalization allows models to generalize better and make more consistent predictions, even in the face of unusual market conditions.

Assessing the accuracy of financial forecasting models necessitates a comprehensive evaluation utilizing metrics like Mean Squared Error (MSE) and Mean Absolute Error (MAE). MSE, calculated as the average of the squared differences between predicted and actual values, heavily penalizes larger errors, making it sensitive to outliers. Conversely, MAE calculates the average of the absolute differences, offering a more robust measure less affected by extreme values. Utilizing both metrics provides a balanced perspective; a significant disparity between MSE and MAE can indicate the presence of outliers unduly influencing the model’s performance. Therefore, reporting both \text{MSE} = \frac{1}{n}\sum_{i=1}^{n}(y_i - \hat{y}_i)^2 and \text{MAE} = \frac{1}{n}\sum_{i=1}^{n}|y_i - \hat{y}_i| is crucial for a nuanced understanding of a forecasting model’s reliability and its susceptibility to anomalous data points.

Time-MoE, a model architecture designed for temporal forecasting, demonstrates enhanced resilience to outliers when coupled with the Huber Loss function. Traditional loss functions, such as Mean Squared Error, are heavily influenced by extreme values, potentially skewing model training and leading to inaccurate predictions during periods of high volatility. Huber Loss, however, offers a compromise; it behaves like Mean Squared Error for smaller errors, but transitions to Mean Absolute Error as the error magnitude increases, thereby reducing the impact of outliers. This characteristic is particularly valuable in financial time series analysis, where unexpected events can cause significant price fluctuations. By minimizing the influence of these extreme values during training, the incorporation of Huber Loss allows Time-MoE to generate more stable and reliable forecasts, even under turbulent market conditions.

Across a comprehensive evaluation of time series forecasting models (TSFMs), RefineBridge consistently enhances predictive accuracy, as demonstrated by reductions in Mean Squared Error (MSE) ranging from 11% to 71%. This performance improvement extends across diverse model architectures, encompassing various financial assets and forecasting horizons. Rigorous experimentation confirms RefineBridge’s ability to refine predictions, yielding more reliable and precise forecasts compared to baseline TSFMs. The consistent and substantial nature of these MSE reductions highlights RefineBridge’s potential to significantly improve forecasting capabilities in practical financial applications, offering a valuable tool for analysts and decision-makers.

Extensive experimentation reveals a consistently strong performance for RefineBridge across a diverse range of forecasting tasks. Across ninety distinct experimental configurations – varying models, financial assets, and prediction horizons – the method demonstrably improved forecasting accuracy in eighty-one instances. This substantial success rate highlights RefineBridge’s robustness and generalizability, suggesting it is not merely optimized for specific scenarios but offers a broad enhancement to time series forecasting methodologies. The consistent gains observed across this comprehensive evaluation underscore its potential as a valuable addition to the toolkit of financial analysts and researchers.

The efficiency of RefineBridge is a notable aspect of its performance gains; it consistently elevates forecasting accuracy while maintaining a remarkably small model size. With only 2.3 million parameters, RefineBridge significantly undercuts the parameter count of comparable Low-Rank Adaptation (LoRA) methods – specifically, LoRA implementations applied to Chronos (7.6M parameters), Moirai (2.4M parameters), and Time-MoE (2.7M parameters). This streamlined architecture not only reduces computational demands during training and inference but also minimizes the risk of overfitting, contributing to its robust and generalizable improvements across diverse financial time series forecasting tasks.

The pursuit of accurate financial forecasting, as detailed in this work concerning RefineBridge, echoes a fundamental truth about complex systems: initial conditions, however strong, are rarely sufficient for sustained precision. The model’s approach to refinement, utilizing Schrödinger Bridge optimal transport, recognizes that forecasting isn’t about predicting a single future, but navigating a probability space. This aligns with the wisdom of Barbara Liskov, who observed, “Programs must be right first before they can be efficient.” RefineBridge isn’t merely seeking speed; it’s prioritizing the correctness of forecasts through iterative refinement, acknowledging that even foundation models benefit from a continuous process of adaptation and correction. The consistent improvement over methods like LoRA demonstrates that delaying fixes-or in this case, refinements-imposes a tax on the ambition of creating truly robust predictive systems.

What’s Next?

RefineBridge, as a post-processing step, acknowledges an inherent temporality in even the most advanced forecasting systems. It does not promise to prevent decay – the inevitable divergence between model prediction and actualized time – but rather to manage it, to offer a more graceful descent into uncertainty. The improvement over LoRA is not a victory, but a postponement. Every bug in the refined forecast, every deviation from reality, remains a moment of truth in the timeline, a signal of the system’s aging.

The reliance on optimal transport, while elegant, introduces its own set of constraints. The ‘cost’ function, the definition of ‘similarity’ between probabilistic distributions, is itself a temporal artifact. Future work must grapple with the meta-problem of evolving cost functions – how does the very definition of accuracy change over time, particularly in the notoriously non-stationary realm of financial data?

Ultimately, the field is not converging on perfect prediction, but on increasingly sophisticated methods of managing its impossibility. Technical debt, in this context, isn’t simply a coding oversight; it’s the past’s mortgage paid by the present, and RefineBridge, for all its ingenuity, is merely another payment plan. The challenge remains: not to build systems that resist time, but to design them to age with a degree of resilience, and perhaps, even a kind of dignified acceptance.

Original article: https://arxiv.org/pdf/2512.21572.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2025-12-29 16:05