Predicting the Future, One Step at a Time

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Author: Denis Avetisyan

A new forecasting approach decouples prediction horizons to achieve more stable and accurate long-term time series analysis.

Evolutionary Forecasting leverages historical observations - represented as foundational data - to iteratively refine predictive models, establishing a cyclical process of analysis and improvement.
Evolutionary Forecasting leverages historical observations – represented as foundational data – to iteratively refine predictive models, establishing a cyclical process of analysis and improvement.

Evolutionary Forecasting addresses the limitations of direct forecasting by optimizing for variable-length output sequences.

Despite advances in long-term time series forecasting, models often struggle to extrapolate accurately beyond the training horizon due to conflicting optimization signals. This work, ‘To See Far, Look Close: Evolutionary Forecasting for Long-term Time Series’, introduces a novel paradigm-Evolutionary Forecasting (EF)-that decouples prediction and evaluation horizons, revealing a counterintuitive finding: models trained on shorter horizons outperform those directly trained on long horizons. By reframing forecasting as an evolutionary process, we demonstrate that traditional Direct Forecasting is a limited case within a broader generative framework, mitigating gradient conflicts and enabling robust asymptotic stability. Could this shift from static mapping to autonomous evolutionary reasoning unlock a new era of foundation models for time series analysis?

The Inherent Challenges of Extrapolating into the Unknown

Predicting trends far into the future – long-term time series forecasting – underpins crucial decision-making across diverse fields, from economic planning and resource management to climate modeling and public health. Despite its importance, achieving accuracy over extended horizons presents a significant challenge; unlike short-term predictions where recent patterns often dominate, long-term forecasts are susceptible to the compounding effects of unpredictable events and the inherent instability of complex systems. This difficulty isn’t merely a matter of refining existing techniques, but stems from the fundamental limitations of extrapolating from finite historical data into an uncertain future, demanding innovative approaches that acknowledge and account for the possibility of unforeseen shifts and systemic changes.

Traditional time series forecasting often relies on recursive methods, where predictions are made incrementally, using prior forecasts as inputs for subsequent ones. While seemingly straightforward, this approach is fundamentally susceptible to error accumulation. Each predictive step introduces a degree of uncertainty, and because these errors are compounded with each iteration, even minor inaccuracies can rapidly escalate over extended forecasting horizons. This phenomenon severely limits the reliability of long-term predictions, as the model effectively propagates and amplifies its initial imprecision. Consequently, recursive methods, despite their simplicity, struggle to maintain accuracy when predicting far into the future, necessitating the development of more robust techniques capable of mitigating error propagation and preserving predictive power.

Direct forecasting struggles with long-horizon tasks due to error accumulation, necessitating a recurrent or stateful approach to maintain consistent predictions.
Direct forecasting struggles with long-horizon tasks due to error accumulation, necessitating a recurrent or stateful approach to maintain consistent predictions.

Direct Forecasting: A Paradigm Shift in Temporal Prediction

Direct Forecasting addresses limitations of autoregressive methods by generating predictions for all future time steps in a single forward pass through the model. Traditional autoregressive approaches, which predict one step at a time, suffer from error accumulation as errors from earlier predictions propagate and amplify with each subsequent step. By contrast, Direct Forecasting calculates all future values simultaneously, eliminating this sequential error propagation. This is achieved by framing the long-term forecasting task as a single, direct prediction problem, allowing the model to consider the entire forecast horizon during each forward pass and reducing the impact of initial prediction errors on subsequent steps.

The Informer model, introduced in 2020, was the first to implement Direct Forecasting within a Transformer architecture for long sequence time-series forecasting. Unlike traditional autoregressive methods that predict one step at a time, Informer predicts the entire future sequence in a single forward pass. This is achieved through the use of ProbSparse Self-Attention, which reduces the quadratic complexity of standard self-attention to linear complexity, enabling efficient processing of long sequences. Experimental results demonstrated that Informer outperformed established state-of-the-art models, including Transformer, LSTM, and DeepAR, on a variety of long-sequence forecasting tasks, specifically in areas like electricity transformer load and traffic flow prediction, validating the effectiveness of the Direct Forecasting paradigm.

Direct Forecasting, while offering advantages in long-term prediction, is susceptible to a phenomenon termed Distal Dominance. This occurs because gradients calculated during backpropagation from distant future time steps can exhibit significantly larger magnitudes than those from nearer steps, effectively overshadowing the learning signal for short-term predictions. Quantitative analysis, specifically the calculation of cosine similarity between gradient segments corresponding to different forecast horizons, demonstrates this conflict; results frequently show near-zero or negative cosine similarity values, indicating that gradients from disparate segments are orthogonal or opposing, hindering effective optimization of the model for all time horizons.

Training models directly with the evaluation horizon of 96 time steps yields lower mean squared error than truncating longer forecasts to that horizon, demonstrating that truncation compromises performance on real-world datasets.
Training models directly with the evaluation horizon of 96 time steps yields lower mean squared error than truncating longer forecasts to that horizon, demonstrating that truncation compromises performance on real-world datasets.

Evolutionary Forecasting: Decoupling Horizons for Robust Extrapolation

Evolutionary Forecasting differentiates itself from Direct Forecasting by independently managing the Output Horizon and the Evaluation Horizon. Direct Forecasting typically evaluates a single, long-term prediction; in contrast, Evolutionary Forecasting optimizes predictions across multiple, shorter Evaluation Horizons within the broader Output Horizon. This means the model doesn’t attempt to directly predict the entire future sequence at once. Instead, it iteratively refines predictions over shorter time steps – the Evaluation Horizon – and chains these shorter predictions together to fulfill the longer Output Horizon. This decoupling allows for more granular optimization and avoids the challenges associated with optimizing a single, extended forecast.

Decoupling the Output and Evaluation Horizons in Evolutionary Forecasting facilitates iterative reasoning by enabling the model to refine predictions incrementally. This contrasts with Direct Forecasting, where a single prediction is made for the entire forecast horizon. The iterative approach improves extrapolation, especially when forecasting beyond the span of available historical data, as the model can build upon its own recent predictions rather than attempting to directly map distant future values. This capability is critical because performance in standard time series forecasting often degrades rapidly when extrapolating beyond observed data ranges; iterative refinement mitigates this effect by allowing the model to progressively extend its predictions based on shorter-term evaluations.

Optimizing for shorter evaluation horizons in Evolutionary Forecasting mitigates common issues found in Direct Forecasting, specifically gradient conflicts and distal dominance. Gradient conflicts arise when optimizing over extended prediction lengths, causing instability during training. Distal dominance occurs when early time steps disproportionately influence the loss function, overshadowing later, potentially more relevant data. By focusing on shorter-term predictive accuracy, the model reduces these effects, leading to improved extrapolation and a demonstrated relative precision improvement of up to 13.92% in time series forecasting benchmarks compared to standard Direct Forecasting approaches.

Statistical dominance analysis reveals that models employing a non-default feedback mechanism (L≠HL≠H) consistently outperform those using the conventional default feedback (<span class="katex-eq" data-katex-display="false">L=HL=H</span>) across varying input lengths, as demonstrated by a higher win ratio and optimal performance probability distribution.
Statistical dominance analysis reveals that models employing a non-default feedback mechanism (L≠HL≠H) consistently outperform those using the conventional default feedback (L=HL=H) across varying input lengths, as demonstrated by a higher win ratio and optimal performance probability distribution.

Towards a Foundation for Generalizable Temporal Intelligence

Evolutionary Forecasting represents a fundamental shift in time series modeling, moving beyond incremental improvements to existing techniques and establishing a crucial building block for future Foundation Models. Unlike traditional approaches that directly predict outcomes for a specific horizon, this paradigm embraces iterative refinement; a model progressively evolves its forecasts over multiple steps, learning to correct its own errors and adapt to complex temporal dependencies. This methodology mirrors the way humans reason about future events – not as a single, static prediction, but as a dynamic process of assessment and adjustment. Consequently, Evolutionary Forecasting isn’t merely about enhancing accuracy; it’s about cultivating a more flexible and robust intelligence capable of handling the inherent uncertainty and variability within time series data, ultimately paving the way for models that generalize effectively across diverse forecasting tasks and datasets.

A significant advancement in time series forecasting centers on a shift from predicting fixed, distant horizons to an evolutionary approach. This methodology decouples the forecasting horizon from the model itself, enabling iterative refinement of predictions over time. Rather than a single, direct attempt to forecast far into the future, the model progressively builds upon its previous outputs, adapting and improving with each step. This paradigm has demonstrably outperformed traditional Direct Forecasting techniques, achieving a win ratio exceeding 80% across a range of datasets and varying input lengths. The capacity to iteratively reason and adjust forecasts positions Evolutionary Forecasting as a foundational element in developing more adaptable and generalizable time series intelligence, offering resilience and improved accuracy even when dealing with complex, long-term predictions.

The integration of teacher forcing within the evolutionary forecasting framework significantly refines the training process, yielding improvements in both model performance and its capacity to generalize to unseen data. This technique, where the model is guided by ground truth data during training, fosters more accurate predictions and accelerates learning. Crucially, this approach demonstrates remarkable stability even when forecasting across extended time horizons – a domain where traditional direct forecasting methods frequently encounter catastrophic failures. By mitigating the accumulation of errors inherent in long-range predictions, teacher forcing enables the model to maintain reliable performance and robustly navigate the complexities of extreme horizon forecasting, ultimately unlocking the potential for truly generalizable time series intelligence.

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The pursuit of accurate long-term forecasting, as detailed in this work on Evolutionary Forecasting, echoes a fundamental principle of mathematical elegance. The separation of output and evaluation horizons in EF isn’t merely a technical adjustment, but a striving for provable stability-a method designed to minimize the accumulation of error inherent in extrapolation. As Ken Thompson aptly stated, “Sometimes it’s better to rewrite the code than to debug it.” This resonates with the EF approach; rather than endlessly refining Direct Forecasting to address its limitations, the authors fundamentally redesigned the forecasting paradigm, seeking a more robust and mathematically sound solution. The inherent gradient conflict in long-term predictions demands such a principled re-evaluation.

What Lies Ahead?

The decoupling of output and evaluation horizons, as demonstrated by Evolutionary Forecasting, presents a necessary, if not entirely sufficient, corrective to the persistent instability plaguing long-term time series prediction. The field has long favored empirical success over theoretical grounding; optimization pursued without rigorous analysis is, predictably, a path to brittle, overfitted models. While initial results are promising, the true test will lie in extending this framework beyond the carefully curated datasets that often mask fundamental limitations.

A critical area for future investigation concerns the nature of ‘gradient conflict’ itself. The paper rightly identifies this as a source of divergence, but a deeper mathematical understanding of its origins-and, crucially, its inevitability-remains elusive. Is complete elimination even possible, or must practitioners accept it as a constant, requiring novel regularization techniques beyond those currently employed? Furthermore, the potential interplay between Evolutionary Forecasting and the emerging paradigm of foundation models deserves careful scrutiny. Can the strengths of both be combined, or will the inherent limitations of one ultimately constrain the other?

Ultimately, the pursuit of increasingly accurate long-term forecasts is not merely a technical challenge, but a philosophical one. It forces a confrontation with the limits of predictability itself. The elegance of a solution, after all, resides not in its ability to chase an asymptote, but in its capacity to reveal the fundamental constraints that govern the system under observation.

Original article: https://arxiv.org/pdf/2601.23114.pdf

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

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2026-02-02 17:51