Forecasting the Future with Language: A New Approach to Time Series Analysis

Author: Denis Avetisyan

Researchers are leveraging the power of large language models to predict future trends in time series data, even when data is limited.

LoFT-LLM establishes a training pipeline where a low-frequency learner first processes filtered ground truth, followed by a residual learner trained with the first fixed, and ultimately, a large language model is fine-tuned using prompts constructed from both learners and auxiliary information to produce final predictions.

LoFT-LLM combines frequency domain analysis with semantic calibration to improve the accuracy and interpretability of low-frequency time series forecasting.

Accurate time-series forecasting is often hampered by limited data and the obscuring effects of high-frequency noise. This paper introduces LoFT-LLM: Low-Frequency Time-Series Forecasting with Large Language Models, a novel framework that leverages frequency-domain analysis and semantic calibration with large language models to address these challenges. By isolating stable low-frequency trends and refining predictions with contextual knowledge, LoFT-LLM demonstrably outperforms existing methods, particularly in data-scarce scenarios. Could this approach unlock more robust and interpretable forecasting across diverse real-world applications, from finance to energy?

Unveiling Temporal Dependencies: The Core Challenge

Conventional time series analysis techniques, such as autoregressive integrated moving average (ARIMA) models and exponential smoothing, frequently exhibit limitations when tasked with identifying and leveraging relationships between data points separated by significant intervals. These methods typically rely on identifying patterns within a limited, recent history, making them less effective when forecasting events influenced by factors deeply embedded in the past. The core challenge lies in their inability to retain and process information from distant historical data without substantial loss of signal or increased computational complexity; this often leads to diminished accuracy when predicting outcomes dependent on these long-range dependencies, particularly in complex systems where subtle, delayed effects can be crucial for accurate projections.

Despite the promise of deep learning architectures, such as transformers, in enhancing time series forecasting, practical limitations exist. These models, renowned for their ability to capture complex relationships, often demand substantial computational resources, hindering their deployment in real-time applications or on limited hardware. Furthermore, the core mechanism of transformers – parallel processing of all time steps – clashes with the intrinsic sequential dependence present in time series data. This necessitates modifications, like positional encoding, to inject temporal information, yet these adaptations don’t fully address the challenge of efficiently modeling the order of events. Consequently, while transformers demonstrate improved capacity, their computational cost and difficulty adapting to sequential data present significant hurdles to widespread adoption in time series analysis.

Accurate time series forecasting hinges on a model’s ability to disentangle and represent data at multiple timescales. Short-term fluctuations, often representing noise or immediate reactions, require sensitivity to recent history, while underlying long-term trends reveal fundamental patterns and future direction. A successful forecasting system doesn’t simply average past values; it dynamically weights these contributions, allowing transient effects to diminish and persistent trends to dominate predictions. This necessitates architectures capable of selectively attending to relevant historical information, effectively filtering out noise and amplifying signals indicative of lasting change – a capability crucial for applications ranging from financial market prediction to climate modeling and resource management. The challenge lies in building models that are both responsive to immediate changes and grounded in the broader historical context, achieving a balance between detail and generalization.

Low-pass filtering of noisy time series data reveals dominant low-frequency trends that serve as supervisory signals for a frequency-aware learning approach.

The Primacy of Low-Frequency Signals

Low-frequency learning in time series analysis centers on identifying and modeling the persistent, cyclical components that exhibit gradual changes over extended periods. These low-frequency patterns, representing the underlying trends and seasonality, typically contain the most significant predictive power as they are less susceptible to short-term noise and random fluctuations. Accurate capture of these dominant patterns is foundational for robust forecasting, as models built upon them are better equipped to generalize to future data and provide reliable predictions. The amplitude of low-frequency components often dwarfs that of higher-frequency noise, making their isolation and modeling a primary objective in time series decomposition and analysis.

The Discrete Fourier Transform (DFT) is a computational method used to decompose a time series into its constituent frequencies. Given a time series $x_0, x_1, …, x_{N-1}$, the DFT transforms it into a sequence of complex numbers $X_k$, where $k$ represents a specific frequency. The magnitude of $X_k$ indicates the strength of that frequency in the original signal, and the phase indicates its relative timing. By analyzing the resulting frequency spectrum, dominant low-frequency components can be identified and isolated. These components can then be modeled separately, or used to reconstruct a smoothed version of the original time series, effectively filtering out higher-frequency noise and allowing for targeted analysis and prediction based on the underlying trends.

Prioritizing low frequencies in time series analysis directly addresses the signal-to-noise ratio. High-frequency components often represent short-term fluctuations or noise, while low-frequency components capture the underlying, persistent trends. By focusing model parameters and computational resources on accurately representing these lower frequencies, the influence of noisy, high-frequency data is diminished. This targeted approach leads to improved model accuracy, as predictions are based on the dominant patterns rather than transient variations. Furthermore, reducing the complexity required to model high-frequency noise enhances computational efficiency, decreasing processing time and resource consumption without sacrificing predictive power.

LoFT-LLM utilizes a residual learning structure with a configurable backbone predictor and a training pipeline incorporating components highlighted for clarity, enabling adaptable learning through its PLFM.

LoFT-LLM: A Phased Approach to Forecasting

LoFT-LLM utilizes a three-phase forecasting framework designed to address the challenges inherent in time series prediction. The initial phase, low-frequency learning, focuses on modeling the dominant, long-term trends within the data. This is followed by residual learning, which captures the remaining high-frequency variations not accounted for by the low-frequency component. Finally, LLM calibration leverages large language models to refine the combined low-frequency and residual predictions by incorporating contextual information and improving overall forecast robustness. This sequential approach allows for a more comprehensive and accurate representation of the time series data compared to single-stage forecasting methods.

The Patch Low-Frequency Forecasting Module employs the Frequency Alignment Loss ($L_{FA}$) to enhance the capture of low-frequency dependencies within time series data. This loss function directly minimizes the discrepancy between the frequency spectra of the predicted and actual time series, ensuring that the model accurately represents the dominant, slower-varying components. By focusing on spectral alignment, $L_{FA}$ mitigates error accumulation over longer forecast horizons, as inaccuracies in low-frequency components significantly impact long-term prediction accuracy. The module divides the input time series into patches, allowing for localized frequency analysis and improved representation of non-stationary low-frequency patterns, thereby contributing to more robust and accurate long-term forecasts.

Residual learning addresses the limitations of low-frequency modeling by explicitly capturing high-frequency variations within the time series data. While low-frequency components represent broader trends, residual learning focuses on the remaining, more granular fluctuations not accounted for by the initial model. This is achieved by calculating the difference between the actual time series values and the predictions made by the low-frequency model, effectively isolating the high-frequency residuals. By modeling these residuals separately, the forecasting framework gains a more complete representation of the time series, leading to improved short-term accuracy and a better overall capture of complex temporal dynamics. This complementary approach allows for a more nuanced understanding and prediction of the time series behavior than either method alone.

LLM Calibration functions as a final refinement stage within the LoFT-LLM framework, leveraging the capabilities of Large Language Models to incorporate contextual data into the forecasting process. This module receives both the low-frequency and residual predictions, along with relevant external variables representing contextual information such as promotional events, economic indicators, or weather patterns. The LLM then processes these combined inputs to generate a calibrated forecast, effectively adjusting the initial predictions based on the identified contextual influences. This calibration step aims to correct for biases present in the low-frequency and residual components, and to improve the model’s responsiveness to dynamic external factors, ultimately increasing both the accuracy and robustness of the final time series forecast.

The input prompt used to calibrate the language model on the FundAR dataset provides context for generating responses related to financial reasoning.

Demonstrated Performance and Broad Applicability

LoFT-LLM demonstrates robust performance across diverse time series forecasting challenges, extending beyond theoretical potential into practical application. The model has been rigorously tested on real-world datasets, notably achieving accurate predictions for both solar power generation – a critical component of renewable energy management – and fund flow forecasting, vital for financial analysis and investment strategies. This success isn’t limited to a single domain; the framework’s adaptability allows it to effectively model the complex temporal dependencies inherent in these disparate data types, highlighting its potential for broader implementation in fields ranging from energy economics to financial modeling and beyond. The consistent results across the Solar and FundAR datasets underscore LoFT-LLM’s capacity to generalize and provide reliable forecasts in varied, complex scenarios.

Rigorous evaluation using standard time series forecasting metrics consistently reveals LoFT-LLM’s enhanced predictive capabilities. Analyses employing $Root Mean Squared Error$ (RMSE), $Mean Absolute Error$ (MAE), and $Mean Absolute Percentage Error$ (MAPE) demonstrate that LoFT-LLM outperforms existing forecasting models across diverse datasets. These metrics collectively indicate a substantial reduction in forecasting errors, suggesting that LoFT-LLM not only predicts future values with greater accuracy but also minimizes the magnitude of deviations from actual observations – a critical advantage for applications requiring precise and reliable time series analysis.

Rigorous evaluation of LoFT-LLM across diverse datasets reveals substantial improvements in forecasting accuracy. Specifically, the model demonstrates an average reduction of 26.53% in Mean Absolute Error (MAE) when applied to the FundAR dataset, which tracks fund flow dynamics. Further bolstering these findings, LoFT-LLM achieves a 15.42% average MAE reduction on the Solar dataset, focused on predicting solar power generation. These gains, consistently observed across different time series characteristics, highlight LoFT-LLM’s capacity to capture complex patterns and deliver significantly more precise forecasts compared to existing methodologies. The magnitude of these improvements suggests potential for substantial benefits in practical applications requiring accurate time series prediction, such as financial modeling and renewable energy management.

LoFT-LLM distinguishes itself through a deliberately modular architecture, enabling seamless incorporation with established forecasting methodologies. This design philosophy moves beyond a monolithic approach, allowing practitioners to leverage the strengths of LoFT-LLM in conjunction with their existing toolsets and domain-specific expertise. For example, statistical methods like ARIMA or machine learning models can be readily integrated as preprocessing steps, post-processing refinements, or even parallel pathways within the LoFT-LLM framework. This flexibility isn’t merely a technical feature; it significantly broadens the scope of applicable problems, moving beyond scenarios where a single model might suffice and into complex, multi-faceted forecasting challenges where hybrid approaches yield superior results. Consequently, LoFT-LLM isn’t positioned as a replacement for existing techniques, but rather as a versatile component that enhances and extends their capabilities, unlocking new potential across diverse forecasting applications.

The PLFM forecasting spectrum visualizes performance differences between the FundAR and Solar datasets.

Future Trajectories and Expanding the Horizon

Ongoing investigation centers on developing adaptive methodologies to dynamically balance the contributions of low-frequency and residual learning components within the LoFT-LLM framework. Current approaches often rely on static weighting or predetermined ratios, potentially limiting performance across diverse time series datasets exhibiting varying levels of seasonality and trend. Researchers are exploring techniques – including reinforcement learning and Bayesian optimization – to allow the model to learn the optimal weighting scheme directly from the data, effectively allocating more emphasis to low-frequency patterns when those dominate, and shifting focus to the residual component when finer-grained, high-frequency variations are more prominent. This adaptive capacity promises to enhance the model’s ability to generalize to unseen data and improve forecasting accuracy, particularly in complex scenarios where the relative importance of low- and high-frequency signals fluctuates over time.

The forecasting framework’s performance is poised for refinement through exploration of diverse Large Language Model (LLM) architectures beyond those currently utilized. Researchers are actively investigating how modifications to the foundational LLM-such as varying the number of layers, attention mechanisms, or embedding dimensions-impact the precision and stability of time series predictions. Crucially, this work extends to advanced calibration techniques designed to address potential biases or overconfidence in LLM outputs. These calibration methods, ranging from temperature scaling to more sophisticated distributional calibration, aim to ensure that predicted probabilities accurately reflect the true uncertainty associated with each forecast, ultimately bolstering the framework’s reliability across varying data patterns and forecasting horizons. Improved calibration is expected to provide more trustworthy forecasts, particularly in critical applications where accurate uncertainty quantification is paramount.

The LoFT-LLM framework, initially developed for long-term traffic forecasting, presents a compelling opportunity for broader application across diverse time series domains. Investigations into energy demand forecasting, for example, could leverage LoFT-LLM’s ability to capture complex temporal dependencies and improve prediction accuracy, crucial for grid stability and resource management. Similarly, in financial time series analysis – predicting stock prices, market trends, or economic indicators – the framework’s capacity to integrate both low-frequency patterns and residual learning could potentially enhance forecasting precision and risk assessment. This adaptability suggests that LoFT-LLM isn’t merely a solution for traffic prediction, but a versatile tool for understanding and forecasting complex temporal phenomena across a range of critical industries.

The landscape of time series forecasting is remarkably diverse, with models like FreTS, FreDF, GPT4TS, PatchTST, FITS, and TimeLLM each demonstrating unique strengths in capturing temporal dependencies and patterns. These approaches, ranging from frequency-enhanced transformers to patch-based and fitting-based methodologies, highlight the breadth of viable strategies for predicting future values. Integrating these established models into the LoFT-LLM framework represents a promising avenue for future research, potentially allowing the system to leverage the specific advantages of each, and dynamically select or combine them based on the characteristics of the time series data – ultimately enhancing forecasting accuracy and robustness across a wider range of applications.

The Solar dataset was used to calibrate the large language model with the input prompt shown here.

The pursuit of predictive accuracy often obscures fundamental principles. LoFT-LLM, with its emphasis on frequency domain analysis and semantic calibration, suggests a return to structural honesty. The framework doesn’t simply amass parameters; it distills signal from noise, acknowledging the inherent limitations of data-scarce environments. This resonates with G.H. Hardy’s observation: “A mathematician, like a painter or a poet, is a maker of patterns.” LoFT-LLM isn’t about conjuring forecasts from nothing; it’s about recognizing and extrapolating existing patterns, even when those patterns reside in the low-frequency components of incomplete data.

What Lies Ahead?

The pursuit of forecasting, particularly with the advent of large language models, has often resembled alchemy – a hopeful transmutation of data into legible futures. LoFT-LLM offers a necessary refinement: a focus on the essential frequencies within time series. Yet, the framework’s efficacy, as with all calibrations, remains tethered to the quality of the initial signal. The problem of ‘data-scarce environments’ is not solved by clever architecture, but by the inherent limitations of impoverished observation. Further work must confront this directly, perhaps through synthetic data generation, though such efforts risk compounding the initial errors.

A natural extension lies in exploring the semantic calibration process itself. Currently, it appears reliant on pre-defined prompts. The question arises: can this calibration be automated, allowing the model to discern salient frequencies without explicit instruction? Such a system would represent a genuine shift – a move away from telling the model what to look for, and towards allowing it to discover it. This, however, invites a deeper philosophical consideration: at what point does discovery become mere pattern recognition, devoid of true understanding?

Ultimately, the field must resist the temptation to endlessly layer complexity. The true challenge is not building more elaborate models, but crafting simpler ones that reveal the underlying order within chaos. The merit of LoFT-LLM may not be its absolute predictive power, but its invitation to pare away the superfluous, and to focus on what truly matters: the essential, low-frequency heartbeat of the data itself.

Original article: https://arxiv.org/pdf/2512.20002.pdf

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