Forecasting with Resilience: Learning to Spot What Matters in Time Series

Author: Denis Avetisyan

A new framework enhances time-series forecasting by focusing on aligning learned representations with the deviations most relevant to accurate predictions.

Time-series forecasting must differentiate between input anomalies that are transient and inconsequential to predictions, and those that fundamentally alter the forecasted output, demanding robust anomaly detection capable of discerning their lasting impact.

This work introduces Co-TSFA, a contrastive regularization approach that improves forecasting robustness and anomaly detection by aligning latent representations with forecast-relevant deviations.

Time series forecasting often struggles to differentiate between transient noise and persistent shifts caused by anomalous events, leading to inaccurate predictions. This paper introduces Co-TSFA, a novel ‘Contrastive Time Series Forecasting with Anomalies’ framework that enhances robustness by learning when to ignore or respond to anomalies during forecasting. Co-TSFA achieves this through contrastive regularization, aligning latent representations with forecast-relevant deviations, thereby improving performance under anomalous conditions while maintaining accuracy on normal data. Could this approach pave the way for more reliable time series analysis in real-world applications with inherent uncertainty?

Navigating the Complexities of Time-Series Prediction

The ability to accurately predict future values in a time series – a sequence of data points indexed in time order – underpins effective decision-making across numerous critical sectors. Resource management, for instance, relies on forecasting demand to optimize inventory and prevent shortages, while financial planning utilizes predictive models to assess risk and maximize returns. However, traditional time-series forecasting methods, such as ARIMA and exponential smoothing, often falter when confronted with the inherent complexities of real-world data. These methods frequently assume stationarity – that the statistical properties of the series remain constant over time – a condition rarely met in dynamic systems. Furthermore, they struggle to accommodate non-linear relationships, evolving trends, and the unpredictable shocks that characterize many real-world processes, leading to forecasts with limited accuracy and practical utility. Consequently, a persistent need exists for more robust and adaptive forecasting techniques capable of navigating these challenges and delivering reliable predictions in complex environments.

The inherent dynamism of real-world data often manifests as non-stationarity in time series, meaning statistical properties like mean and variance shift over time – a critical impediment to accurate forecasting. Traditional models, frequently predicated on the assumption of consistent data characteristics, struggle to adapt to these evolving patterns, leading to diminished predictive power. Further complicating matters is the inevitable presence of anomalies – unexpected events or outliers – which can dramatically skew forecasts if not properly identified and addressed. These anomalies aren’t simply random noise; they can signal genuine shifts in the underlying system, demanding sophisticated detection algorithms and adaptive modeling techniques to maintain forecast reliability. Effectively handling both non-stationarity and anomalies is therefore paramount to building robust time-series predictions capable of navigating the complexities of real-world phenomena and providing actionable insights.

Many established time-series forecasting methods exhibit a concerning lack of resilience when faced with real-world volatility. These approaches, often meticulously calibrated to historical data, frequently demonstrate a limited capacity to generalize beyond those specific conditions. Unexpected disruptions – such as sudden economic shocks, novel consumer behaviors, or even the introduction of new policies – can quickly invalidate the underlying assumptions of these models, leading to substantial forecast errors. This brittleness stems from an over-reliance on stationarity – the assumption that the statistical properties of the time series remain constant over time – which rarely holds true in complex dynamic systems. Consequently, models trained on past data may struggle to adapt to shifts in underlying patterns, rendering them unreliable predictors in rapidly evolving environments and highlighting the need for more robust and adaptive forecasting techniques.

ATM transaction volumes exhibit high volatility and lack predictable temporal patterns, as demonstrated by sharp spikes and inconsistent activity across randomly selected machines.

Enhancing Forecast Robustness with Contrastive Time-Series Analysis

Co-TSFA (Contrastive Time-Series Forecasting Architecture) introduces a regularization framework designed to improve the resilience of time-series forecasting models to anomalous data. Traditional forecasting methods often exhibit performance degradation when presented with inputs containing outliers or unexpected patterns. Co-TSFA mitigates this by learning robust representations, meaning the model prioritizes features that are consistent across various plausible inputs, rather than being overly sensitive to individual data points. This is achieved through a contrastive learning approach, where the model is trained to minimize the distance between representations of similar time series and maximize the distance between representations of dissimilar ones, effectively building a more stable and generalized internal model of the underlying data generating process. The resulting representations are less likely to be distorted by anomalies, leading to improved forecasting accuracy and reliability in the presence of noisy or corrupted data.

Contrastive learning, as implemented in Co-TSFA, operates by training the model to maximize the similarity of embeddings for normal time-series data while minimizing the similarity between normal data and anomalous instances. This is achieved through the creation of positive and negative pairs; positive pairs consist of different augmentations of the same normal time series, while negative pairs are formed using anomalous data or significantly different normal time series. The model learns to project these pairs into a latent space where positive pairs are close together and negative pairs are distant, effectively creating a boundary between normal and anomalous patterns. This differentiation enhances the model’s ability to identify and mitigate the impact of disruptions, as it has explicitly learned to recognize deviations from established norms within the time-series data.

Latent representation alignment within the Co-TSFA framework enforces a direct correspondence between variations in the learned latent space and consequential changes in the forecasted output. This is achieved by minimizing the distance between latent representations of similar time-series segments while maximizing the distance between dissimilar segments, effectively creating a structured latent space. Consequently, interpretable relationships emerge, where specific directions or magnitudes of change within the latent space predictably affect the forecasted values. This alignment enhances the reliability of the model by reducing the potential for unpredictable or spurious correlations between latent features and the output, and facilitates analysis of the model’s internal reasoning process.

Co-TSFA utilizes a pipeline to identify both positive and negative pairs for improved performance.

Distinguishing Anomaly Types for Comprehensive Detection

Co-TSFA (Contextual Time Series Forecasting Anomaly detection) distinguishes between two primary anomaly types: input-only and input-output. Input-only anomalies represent deviations in the input data that do not influence the forecasted values; these are detected through contextual analysis without impacting predictive accuracy. Conversely, input-output anomalies are those where input deviations do propagate into the forecasted output, creating discrepancies between predicted and actual values. Co-TSFA is engineered to effectively identify both types by analyzing the contextual relationships within the time series data and assessing the impact of input variations on subsequent predictions, enabling comprehensive anomaly detection regardless of propagation.

To improve generalization to previously unseen anomalous patterns, the Co-TSFA framework incorporates data augmentation techniques. These techniques synthetically expand the training dataset by creating modified versions of existing anomalous input sequences. Specifically, the framework utilizes methods such as adding noise, scaling, and time warping to the anomalous data. This process increases the diversity of the training data, enabling the model to learn more robust representations of anomalies and improve its ability to detect and handle novel anomalous patterns during inference. The augmented data helps the model overcome limitations imposed by the finite size and potential biases of the original training dataset, thereby enhancing its overall performance and adaptability.

Performance validation of the Co-TSFA model was conducted using datasets representing traffic patterns, cash demand forecasting, and electricity consumption. Across these diverse datasets and various anomaly types, Co-TSFA consistently demonstrated a reduction in both Mean Absolute Error (MAE) and Mean Squared Error (MSE). Quantitative results indicate that the model achieves statistically significant improvements over baseline methods in anomaly detection and forecasting accuracy, confirming its broad applicability to time-series anomaly handling in different domains. Specifically, reductions in MAE and MSE were observed across all tested datasets, with the magnitude of improvement varying depending on the dataset characteristics and anomaly type.

The Co-TSFA alignment loss consistently decreased during training, with each step representing progress after processing ten batches of data.

Building Upon Established Architectures for Enhanced Performance

Co-TSFA demonstrates compatibility with and performance gains when integrated with multiple established time-series forecasting models. Specifically, it has been successfully implemented with Autoformer, TimesNet, TimeXer, iTransformer, and Informer architectures. This compatibility allows for the enhancement of existing forecasting pipelines without requiring a complete model overhaul. Integration involves incorporating Co-TSFA’s anomaly detection capabilities as a preprocessing or post-processing step, or by directly modifying the input features utilized by these models. The modular design of Co-TSFA facilitates its use alongside these diverse architectures, enabling a flexible approach to time-series forecasting with integrated anomaly handling.

The Transformer architecture, central to models like Autoformer and Informer, utilizes self-attention mechanisms to weigh the importance of different parts of the input sequence when making predictions. Unlike recurrent neural networks (RNNs) which process data sequentially, Transformers can process the entire input sequence in parallel, significantly reducing training time. This parallelization, coupled with the attention mechanism, enables the model to efficiently capture long-range dependencies – relationships between data points that are far apart in the sequence – without the vanishing gradient problems often encountered in RNNs. The attention mechanism calculates a weighted sum of input embeddings, where the weights are determined by the relevance of each input element to the current prediction, effectively allowing the model to focus on the most pertinent information within the time series.

Performance evaluation utilized standard time-series forecasting metrics including Mean Absolute Error ($MAE$), Mean Squared Error ($MSE$), and Symmetric Mean Absolute Percentage Error ($SMAPE$). Results demonstrate consistent performance improvements for Co-TSFA across a variety of datasets and anomaly types when compared to the RobustTSF model. Gains are most significant in Input+Output forecasting settings, and statistical significance, as determined by a p-value of less than 0.01, was achieved on the ETTh1 dataset, indicating a reliable and demonstrable improvement in forecasting accuracy.

Stable training and validation losses indicate successful optimization throughout the training process.

Towards Resilient and Reliable Forecasting Systems

Conventional time-series forecasting approaches often struggle with unexpected disruptions – anomalies – leading to inaccurate predictions and potentially costly errors. The Co-TSFA framework directly confronts this challenge by integrating a robust anomaly handling system into the forecasting process. Unlike methods that treat anomalies as noise to be filtered, Co-TSFA identifies and incorporates these deviations, allowing the model to adapt and maintain accuracy even amidst irregular data patterns. This is achieved through a novel combination of statistical analysis and machine learning, enabling the system to distinguish between genuine anomalies and random fluctuations. Consequently, forecasts generated by Co-TSFA demonstrate enhanced reliability and precision, particularly in dynamic environments where unpredictable events are common, offering a significant step towards more resilient and trustworthy predictive systems.

The enhanced forecasting capabilities offered by Co-TSFA extend far beyond theoretical improvements, promising tangible benefits across diverse sectors. In resource management, more accurate predictions of demand allow for optimized allocation of essential supplies like water and energy, minimizing waste and ensuring availability. Similarly, within financial planning, the system’s reliability can refine investment strategies, mitigate risks, and improve portfolio performance through more precise market projections. Perhaps most crucially, Co-TSFA’s ability to anticipate disruptions offers a transformative advantage to supply chain optimization; by proactively identifying potential bottlenecks or delays, businesses can adapt strategies, diversify sourcing, and maintain seamless operations, ultimately bolstering resilience in an increasingly volatile global landscape.

The potential of Co-TSFA extends beyond its initial applications, prompting future investigations into diverse fields such as climate modeling, healthcare monitoring, and industrial process control. Researchers aim to adapt the framework to accommodate the unique characteristics and challenges presented by these new domains, potentially unlocking improved predictive capabilities where accurate time-series analysis is critical. Simultaneously, ongoing development focuses on refining anomaly detection methods, moving beyond simple thresholding to incorporate machine learning algorithms capable of identifying subtle, complex patterns indicative of unusual system behavior. This includes exploring techniques for real-time anomaly detection and prediction, allowing for proactive intervention and mitigation of potential disruptions, ultimately bolstering the robustness and dependability of forecasting systems across numerous disciplines.

Increasing the regularization parameter λCL consistently reduces both the mean absolute error and mean squared error under anomalous conditions for both input-only and input-to-output configurations.

The pursuit of robust time-series forecasting, as demonstrated by Co-TSFA, necessitates a holistic understanding of system behavior. This work champions the idea that improvements aren’t achieved through isolated fixes, but rather through aligning latent representations with forecast-relevant deviations. As Robert Tarjan once noted, “Structure dictates behavior.” This sentiment echoes throughout the paper, where the careful construction of a contrastive regularization framework allows the model to evolve its understanding of time-series data without requiring a complete overhaul. By focusing on representation alignment, Co-TSFA strengthens the system’s capacity to handle anomalies-a testament to the power of well-defined structure in complex systems.

Beyond the Forecast Horizon

The pursuit of robust time-series forecasting, as exemplified by this work, perpetually reveals a humbling truth: prediction is not about capturing ‘the’ future, but about building systems resilient to the inevitable deviations. Co-TSFA’s approach, aligning latent representations with forecast-relevant anomalies, is a step towards this resilience, yet introduces its own set of trade-offs. The very definition of ‘relevance’-what constitutes a meaningful deviation-remains context-dependent and, ultimately, subjective. A simplification in defining this relevance, while computationally convenient, inevitably introduces a cost in capturing the full spectrum of possible anomalies.

Future work must address the limitations inherent in relying solely on deviations from forecasts. The system’s ability to extrapolate beyond the observed data – to anticipate novel anomalies, not just react to known variations – remains a significant challenge. Perhaps the most fruitful avenue lies in integrating causal reasoning. A model that understands why a time series behaves as it does, rather than simply how it does, will be far better equipped to handle unforeseen circumstances, reducing the reliance on purely contrastive regularization.

Ultimately, the goal is not simply to minimize forecasting error, but to build models that gracefully degrade in the face of uncertainty. This requires acknowledging that perfect prediction is an illusion, and that true progress lies in embracing the inherent complexity of the systems being modeled. The elegance of any solution will be measured not by its cleverness, but by its capacity to navigate the inevitable imperfections of reality.

Original article: https://arxiv.org/pdf/2512.11526.pdf

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