Stefan Zohren

Yaxuan Kong, Qingren Yao, Yuqi Nie et al.

Time series data inform critical decisions across many real-world domains. While large language model (LLM) agents can analyze data through natural language and tools, it remains unclear whether they can conduct reliable time series analysis across multi-turn conversations. Existing benchmarks focus on single-step tasks such as forecasting and anomaly detection, overlooking practical workflows where user goals evolve, agents must build on prior analyses, and conclusions emerge from accumulated evidence. In this work, we introduce TimeSage-MT, a multi-turn benchmark for agentic time series reasoning with 240 tasks and 2,680 dialogue turns across 8 real-world domains, spanning basic exploration to decision-oriented analysis. TimeSage-MT is built through a reproducible pipeline that converts real-world time series data into multi-turn conversations with verifiable answers. It provides a unified evaluation protocol and public leaderboard for comparing time series agentic systems. To demonstrate the benchmark's utility, we evaluate frontier LLMs alongside TimeSage, a novel structured agent equipped with a comprehensive time series skill library. The results show sharp performance drops on decision-oriented tasks, driven by failures in memory, uncertainty handling, and domain-based decision making. TimeSage-MT exposes critical gaps in current agentic reasoning and provides a rigorous foundation for future development.

Sascha Frey, Kang Li, Peer Nagy et al.

Financial exchanges across the world use limit order books (LOBs) to process orders and match trades. For research purposes it is important to have large scale efficient simulators of LOB dynamics. LOB simulators have previously been implemented in the context of agent-based models (ABMs), reinforcement learning (RL) environments, and generative models, processing order flows from historical data sets and hand-crafted agents alike. For many applications, there is a requirement for processing multiple books, either for the calibration of ABMs or for the training of RL agents. We showcase the first GPU-enabled LOB simulator designed to process thousands of books in parallel, with a notably reduced per-message processing time. The implementation of our simulator - JAX-LOB - is based on design choices that aim to best exploit the powers of JAX without compromising on the realism of LOB-related mechanisms. We integrate JAX-LOB with other JAX packages, to provide an example of how one may address an optimal execution problem with reinforcement learning, and to share some preliminary results from end-to-end RL training on GPUs.

Felix Drinkall, Stefan Zohren, Janet B. Pierrehumbert

We present a novel approach incorporating transformer-based language models into infectious disease modelling. Text-derived features are quantified by tracking high-density clusters of sentence-level representations of Reddit posts within specific US states' COVID-19 subreddits. We benchmark these clustered embedding features against features extracted from other high-quality datasets. In a threshold-classification task, we show that they outperform all other feature types at predicting upward trend signals, a significant result for infectious disease modelling in areas where epidemiological data is unreliable. Subsequently, in a time-series forecasting task we fully utilise the predictive power of the caseload and compare the relative strengths of using different supplementary datasets as covariate feature sets in a transformer-based time-series model.

Felix Drinkall, Janet B. Pierrehumbert, Stefan Zohren

Large Language Models (LLMs) have been shown to perform well for many downstream tasks. Transfer learning can enable LLMs to acquire skills that were not targeted during pre-training. In financial contexts, LLMs can sometimes beat well-established benchmarks. This paper investigates how well LLMs perform in the task of forecasting corporate credit ratings. We show that while LLMs are very good at encoding textual information, traditional methods are still very competitive when it comes to encoding numeric and multimodal data. For our task, current LLMs perform worse than a more traditional XGBoost architecture that combines fundamental and macroeconomic data with high-density text-based embedding features.

Yaxuan Kong, Zepu Wang, Yuqi Nie et al.

Traditional recurrent neural network architectures, such as long short-term memory neural networks (LSTM), have historically held a prominent role in time series forecasting (TSF) tasks. While the recently introduced sLSTM for Natural Language Processing (NLP) introduces exponential gating and memory mixing that are beneficial for long term sequential learning, its potential short memory issue is a barrier to applying sLSTM directly in TSF. To address this, we propose a simple yet efficient algorithm named P-sLSTM, which is built upon sLSTM by incorporating patching and channel independence. These modifications substantially enhance sLSTM's performance in TSF, achieving state-of-the-art results. Furthermore, we provide theoretical justifications for our design, and conduct extensive comparative and analytical experiments to fully validate the efficiency and superior performance of our model.

Samuel Kessler, Adam Cobb, Tim G. J. Rudner et al.

Sequential Bayesian inference can be used for continual learning to prevent catastrophic forgetting of past tasks and provide an informative prior when learning new tasks. We revisit sequential Bayesian inference and test whether having access to the true posterior is guaranteed to prevent catastrophic forgetting in Bayesian neural networks. To do this we perform sequential Bayesian inference using Hamiltonian Monte Carlo. We propagate the posterior as a prior for new tasks by fitting a density estimator on Hamiltonian Monte Carlo samples. We find that this approach fails to prevent catastrophic forgetting demonstrating the difficulty in performing sequential Bayesian inference in neural networks. From there we study simple analytical examples of sequential Bayesian inference and CL and highlight the issue of model misspecification which can lead to sub-optimal continual learning performance despite exact inference. Furthermore, we discuss how task data imbalances can cause forgetting. From these limitations, we argue that we need probabilistic models of the continual learning generative process rather than relying on sequential Bayesian inference over Bayesian neural network weights. In this vein, we also propose a simple baseline called Prototypical Bayesian Continual Learning, which is competitive with state-of-the-art Bayesian continual learning methods on class incremental continual learning vision benchmarks.

Xingyue Pu, Stephen Roberts, Xiaowen Dong et al.

We investigate the concept of network momentum, a novel trading signal derived from momentum spillover across assets. Initially observed within the confines of pairwise economic and fundamental ties, such as the stock-bond connection of the same company and stocks linked through supply-demand chains, momentum spillover implies a propagation of momentum risk premium from one asset to another. The similarity of momentum risk premium, exemplified by co-movement patterns, has been spotted across multiple asset classes including commodities, equities, bonds and currencies. However, studying the network effect of momentum spillover across these classes has been challenging due to a lack of readily available common characteristics or economic ties beyond the company level. In this paper, we explore the interconnections of momentum features across a diverse range of 64 continuous future contracts spanning these four classes. We utilise a linear and interpretable graph learning model with minimal assumptions to reveal the intricacies of the momentum spillover network. By leveraging the learned networks, we construct a network momentum strategy that exhibits a Sharpe ratio of 1.5 and an annual return of 22%, after volatility scaling, from 2000 to 2022. This paper pioneers the examination of momentum spillover across multiple asset classes using only pricing data, presents a multi-asset investment strategy based on network momentum, and underscores the effectiveness of this strategy through robust empirical analysis.

Xingyue Pu, Stefan Zohren, Stephen Roberts et al.

Network momentum provides a novel type of risk premium, which exploits the interconnections among assets in a financial network to predict future returns. However, the current process of constructing financial networks relies heavily on expensive databases and financial expertise, limiting accessibility for small-sized and academic institutions. Furthermore, the traditional approach treats network construction and portfolio optimisation as separate tasks, potentially hindering optimal portfolio performance. To address these challenges, we propose L2GMOM, an end-to-end machine learning framework that simultaneously learns financial networks and optimises trading signals for network momentum strategies. The model of L2GMOM is a neural network with a highly interpretable forward propagation architecture, which is derived from algorithm unrolling. The L2GMOM is flexible and can be trained with diverse loss functions for portfolio performance, e.g. the negative Sharpe ratio. Backtesting on 64 continuous future contracts demonstrates a significant improvement in portfolio profitability and risk control, with a Sharpe ratio of 1.74 across a 20-year period.

Daniel Poh, Stephen Roberts, Stefan Zohren

Cross-sectional strategies are a classical and popular trading style, with recent high performing variants incorporating sophisticated neural architectures. While these strategies have been applied successfully to data-rich settings involving mature assets with long histories, deploying them on instruments with limited samples generally produce over-fitted models with degraded performance. In this paper, we introduce Fused Encoder Networks -- a novel and hybrid parameter-sharing transfer ranking model. The model fuses information extracted using an encoder-attention module operated on a source dataset with a similar but separate module focused on a smaller target dataset of interest. This mitigates the issue of models with poor generalisability that are a consequence of training on scarce target data. Additionally, the self-attention mechanism enables interactions among instruments to be accounted for, not just at the loss level during model training, but also at inference time. Focusing on momentum applied to the top ten cryptocurrencies by market capitalisation as a demonstrative use-case, the Fused Encoder Networks outperforms the reference benchmarks on most performance measures, delivering a three-fold boost in the Sharpe ratio over classical momentum as well as an improvement of approximately 50% against the best benchmark model without transaction costs. It continues outperforming baselines even after accounting for the high transaction costs associated with trading cryptocurrencies.

Wee Ling Tan, Stephen Roberts, Stefan Zohren

We introduce Spatio-Temporal Momentum strategies, a class of models that unify both time-series and cross-sectional momentum strategies by trading assets based on their cross-sectional momentum features over time. While both time-series and cross-sectional momentum strategies are designed to systematically capture momentum risk premia, these strategies are regarded as distinct implementations and do not consider the concurrent relationship and predictability between temporal and cross-sectional momentum features of different assets. We model spatio-temporal momentum with neural networks of varying complexities and demonstrate that a simple neural network with only a single fully connected layer learns to simultaneously generate trading signals for all assets in a portfolio by incorporating both their time-series and cross-sectional momentum features. Backtesting on portfolios of 46 actively-traded US equities and 12 equity index futures contracts, we demonstrate that the model is able to retain its performance over benchmarks in the presence of high transaction costs of up to 5-10 basis points. In particular, we find that the model when coupled with least absolute shrinkage and turnover regularization results in the best performance over various transaction cost scenarios.

Kieran Wood, Samuel Kessler, Stephen J. Roberts et al.

Forecasting models for systematic trading strategies do not adapt quickly when financial market conditions rapidly change, as was seen in the advent of the COVID-19 pandemic in 2020, causing many forecasting models to take loss-making positions. To deal with such situations, we propose a novel time-series trend-following forecaster that can quickly adapt to new market conditions, referred to as regimes. We leverage recent developments from the deep learning community and use few-shot learning. We propose the Cross Attentive Time-Series Trend Network -- X-Trend -- which takes positions attending over a context set of financial time-series regimes. X-Trend transfers trends from similar patterns in the context set to make forecasts, then subsequently takes positions for a new distinct target regime. By quickly adapting to new financial regimes, X-Trend increases Sharpe ratio by 18.9% over a neural forecaster and 10-fold over a conventional Time-series Momentum strategy during the turbulent market period from 2018 to 2023. Our strategy recovers twice as quickly from the COVID-19 drawdown compared to the neural-forecaster. X-Trend can also take zero-shot positions on novel unseen financial assets obtaining a 5-fold Sharpe ratio increase versus a neural time-series trend forecaster over the same period. Furthermore, the cross-attention mechanism allows us to interpret the relationship between forecasts and patterns in the context set.

Peer Nagy, Sascha Frey, Silvia Sapora et al.

Developing a generative model of realistic order flow in financial markets is a challenging open problem, with numerous applications for market participants. Addressing this, we propose the first end-to-end autoregressive generative model that generates tokenized limit order book (LOB) messages. These messages are interpreted by a Jax-LOB simulator, which updates the LOB state. To handle long sequences efficiently, the model employs simplified structured state-space layers to process sequences of order book states and tokenized messages. Using LOBSTER data of NASDAQ equity LOBs, we develop a custom tokenizer for message data, converting groups of successive digits to tokens, similar to tokenization in large language models. Out-of-sample results show promising performance in approximating the data distribution, as evidenced by low model perplexity. Furthermore, the mid-price returns calculated from the generated order flow exhibit a significant correlation with the data, indicating impressive conditional forecast performance. Due to the granularity of generated data, and the accuracy of the model, it offers new application areas for future work beyond forecasting, e.g. acting as a world model in high-frequency financial reinforcement learning applications. Overall, our results invite the use and extension of the model in the direction of autoregressive large financial models for the generation of high-frequency financial data and we commit to open-sourcing our code to facilitate future research.

Wee Ling Tan, Stephen Roberts, Stefan Zohren

We introduce a novel approach to options trading strategies using a highly scalable and data-driven machine learning algorithm. In contrast to traditional approaches that often require specifications of underlying market dynamics or assumptions on an option pricing model, our models depart fundamentally from the need for these prerequisites, directly learning non-trivial mappings from market data to optimal trading signals. Backtesting on more than a decade of option contracts for equities listed on the S&P 100, we demonstrate that deep learning models trained according to our end-to-end approach exhibit significant improvements in risk-adjusted performance over existing rules-based trading strategies. We find that incorporating turnover regularization into the models leads to further performance enhancements at prohibitively high levels of transaction costs.

Peer Nagy, Jan-Peter Calliess, Stefan Zohren

We employ deep reinforcement learning (RL) to train an agent to successfully translate a high-frequency trading signal into a trading strategy that places individual limit orders. Based on the ABIDES limit order book simulator, we build a reinforcement learning OpenAI gym environment and utilise it to simulate a realistic trading environment for NASDAQ equities based on historic order book messages. To train a trading agent that learns to maximise its trading return in this environment, we use Deep Duelling Double Q-learning with the APEX (asynchronous prioritised experience replay) architecture. The agent observes the current limit order book state, its recent history, and a short-term directional forecast. To investigate the performance of RL for adaptive trading independently from a concrete forecasting algorithm, we study the performance of our approach utilising synthetic alpha signals obtained by perturbing forward-looking returns with varying levels of noise. Here, we find that the RL agent learns an effective trading strategy for inventory management and order placing that outperforms a heuristic benchmark trading strategy having access to the same signal.

Kieran Wood, Stefan Zohren, Stephen J. Roberts

We introduce DeRegiME -- Deep Regime Mixture of Experts -- a direct multi-horizon probabilistic forecaster that separates latent uncertainty regimes from the underlying signal and softly assigns each forecast location to learned recurring regimes using a sparse variational Gaussian process (GP) whose nonstationary regime-mixing kernel and Student-t likelihood combine per-regime sub-kernels and noise processes via a shared gate. This yields a single sparse-GP posterior, not a mixture of GP experts. DeRegiME addresses a key limitation of neural forecasters: point forecasts discard residual uncertainty, and probabilistic heads -- whether single marginals, uninterpreted mixtures, quantile sets, or diffusion samples -- rarely expose the regime structure of the residual. Yet distribution shift in noisy heteroskedastic time series may be abrupt, gradual, or horizon-dependent and often appears in residual uncertainty rather than the conditional mean. DeRegiME yields an interpretable mean-residual-noise decomposition with a direct-sum feature-space representation that anchors regimes as clusters of residual similarity whose transitions surface as implicit changepoints. The effective number of regimes is pruned by the stick-breaking gate. We prove kernel validity and predictive-density propriety, and across ten benchmarks and three encoder grids DeRegiME improves negative log predictive density (NLPD) by 20.3% over the strongest encoder-matched baseline, a DeepAR/GluonTS-style dynamic Student-t head, with parallel gains on CRPS (3.0%) and MSE (4.7%). Improvements are consistent across all datasets, which span abrupt, gradual, and seasonal shifts.

Fernando Moreno-Pino, Stefan Zohren

Volatility forecasts play a central role among equity risk measures. Besides traditional statistical models, modern forecasting techniques based on machine learning can be employed when treating volatility as a univariate, daily time-series. Moreover, econometric studies have shown that increasing the number of daily observations with high-frequency intraday data helps to improve volatility predictions. In this work, we propose DeepVol, a model based on Dilated Causal Convolutions that uses high-frequency data to forecast day-ahead volatility. Our empirical findings demonstrate that dilated convolutional filters are highly effective at extracting relevant information from intraday financial time-series, proving that this architecture can effectively leverage predictive information present in high-frequency data that would otherwise be lost if realised measures were precomputed. Simultaneously, dilated convolutional filters trained with intraday high-frequency data help us avoid the limitations of models that use daily data, such as model misspecification or manually designed handcrafted features, whose devise involves optimising the trade-off between accuracy and computational efficiency and makes models prone to lack of adaptation into changing circumstances. In our analysis, we use two years of intraday data from NASDAQ-100 to evaluate the performance of DeepVol. Our empirical results suggest that the proposed deep learning-based approach effectively learns global features from high-frequency data, resulting in more accurate predictions compared to traditional methodologies and producing more accurate risk measures.

Kunihiro Miyazaki, Takanobu Kawahara, Stephen Roberts et al.

The advancement of large language models (LLMs) has accelerated the development of autonomous financial trading systems. While mainstream approaches deploy multi-agent systems mimicking analyst and manager roles, they often rely on abstract instructions that overlook the intricacies of real-world workflows, which can lead to degraded inference performance and less transparent decision-making. Therefore, we propose a multi-agent LLM trading framework that explicitly decomposes investment analysis into fine-grained tasks, rather than providing coarse-grained instructions. We evaluate the proposed framework using Japanese stock data, including prices, financial statements, news, and macro information, under a leakage-controlled backtesting setting. Experimental results show that fine-grained task decomposition significantly improves risk-adjusted returns compared to conventional coarse-grained designs. Crucially, further analysis of intermediate agent outputs suggests that alignment between analytical outputs and downstream decision preferences is a critical driver of system performance. Moreover, we conduct standard portfolio optimization, exploiting low correlation with the stock index and the variance of each system's output. This approach achieves superior performance. These findings contribute to the design of agent structure and task configuration when applying LLM agents to trading systems in practical settings.

Yaxuan Kong, Yiyuan Yang, Yoontae Hwang et al.

Time series data are foundational in finance, healthcare, and energy domains. However, most existing methods and datasets remain focused on a narrow spectrum of tasks, such as forecasting or anomaly detection. To bridge this gap, we introduce Time Series Multi-Task Question Answering (Time-MQA), a unified framework that enables natural language queries across multiple time series tasks - numerical analytical tasks and open-ended question answering with reasoning. Central to Time-MQA is the TSQA dataset, a large-scale dataset containing $\sim$200k question-answer pairs derived from diverse time series spanning environment, traffic, etc. This comprehensive resource covers various time series lengths and promotes robust model development. We further demonstrate how continually pre-training large language models (Mistral 7B, Llama-3 8B, and Qwen-2.5 7B) on the TSQA dataset enhanced time series reasoning capabilities, moving beyond mere numeric tasks and enabling more advanced and intuitive interactions with temporal data. The complete TSQA dataset, models, user study questionnaires for evaluation, and other related materials have been open-sourced.

Kieran Wood, Stephen J. Roberts, Stefan Zohren

We propose DeePM (Deep Portfolio Manager), a structured deep-learning macro portfolio manager trained end-to-end to maximize a robust, risk-adjusted utility. DeePM addresses three fundamental challenges in financial learning: (1) it resolves the asynchronous "ragged filtration" problem via a Directed Delay (Causal Sieve) mechanism that prioritizes causal impulse-response learning over information freshness; (2) it combats low signal-to-noise ratios via a Macroeconomic Graph Prior, regularizing cross-asset dependence according to economic first principles; and (3) it optimizes a distributionally robust objective where a smooth worst-window penalty serves as a differentiable proxy for Entropic Value-at-Risk (EVaR) - a window-robust utility encouraging strong performance in the most adverse historical subperiods. In large-scale backtests from 2010-2025 on 50 diversified futures with highly realistic transaction costs, DeePM attains net risk-adjusted returns that are roughly twice those of classical trend-following strategies and passive benchmarks, solely using daily closing prices. Furthermore, DeePM improves upon the state-of-the-art Momentum Transformer architecture by roughly fifty percent. The model demonstrates structural resilience across the 2010s "CTA (Commodity Trading Advisor) Winter" and the post-2020 volatility regime shift, maintaining consistent performance through the pandemic, inflation shocks, and the subsequent higher-for-longer environment. Ablation studies confirm that strictly lagged cross-sectional attention, graph prior, principled treatment of transaction costs, and robust minimax optimization are the primary drivers of this generalization capability.

Yoontae Hwang, Stefan Zohren, Yongjae Lee

In the era of rapid globalization and digitalization, accurate identification of similar stocks has become increasingly challenging due to the non-stationary nature of financial markets and the ambiguity in conventional regional and sector classifications. To address these challenges, we examine SimStock, a novel temporal self-supervised learning framework that combines techniques from self-supervised learning (SSL) and temporal domain generalization to learn robust and informative representations of financial time series data. The primary focus of our study is to understand the similarities between stocks from a broader perspective, considering the complex dynamics of the global financial landscape. We conduct extensive experiments on four real-world datasets with thousands of stocks and demonstrate the effectiveness of SimStock in finding similar stocks, outperforming existing methods. The practical utility of SimStock is showcased through its application to various investment strategies, such as pairs trading, index tracking, and portfolio optimization, where it leads to superior performance compared to conventional methods. Our findings empirically examine the potential of data-driven approach to enhance investment decision-making and risk management practices by leveraging the power of temporal self-supervised learning in the face of the ever-changing global financial landscape.

Yaxuan Kong, Hoyoung Lee, Yoontae Hwang et al.

Large Language Models (LLMs) are increasingly integrated into financial workflows, but evaluation practice has not kept up. Finance-specific biases can inflate performance, contaminate backtests, and make reported results useless for any deployment claim. We identify five recurring biases in financial LLM applications. They include look-ahead bias, survivorship bias, narrative bias, objective bias, and cost bias. These biases break financial tasks in distinct ways and they often compound to create an illusion of validity. We reviewed 164 papers from 2023 to 2025 and found that no single bias is discussed in more than 28 percent of studies. This position paper argues that bias in financial LLM systems requires explicit attention and that structural validity should be enforced before any result is used to support a deployment claim. We propose a Structural Validity Framework and an evaluation checklist with minimal requirements for bias diagnosis and future system design. The material is available at https://github.com/Eleanorkong/Awesome-Financial-LLM-Bias-Mitigation.

Adir Saly-Kaufmann, Kieran Wood, Jan Peter-Calliess et al.

We present a large scale benchmark of modern deep learning architectures for a financial time series prediction and position sizing task, with a primary focus on Sharpe ratio optimization. Evaluating linear models, recurrent networks, transformer based architectures, state space models, and recent sequence representation approaches, we assess out of sample performance on a daily futures dataset spanning commodities, equity indices, bonds, and FX spanning 2010 to 2025. Our evaluation goes beyond average returns and includes statistical significance, downside and tail risk measures, breakeven transaction cost analysis, robustness to random seed selection, and computational efficiency. We find that models explicitly designed to learn rich temporal representations consistently outperform linear benchmarks and generic deep learning models, which often lead the ranking in standard time series benchmarks. Hybrid models such as VSN with LSTM, a combination of Variable Selection Networks (VSN) and LSTMs, achieves the highest overall Sharpe ratio, while VSN with xLSTM and LSTM with PatchTST exhibit superior downside adjusted characteristics. xLSTM demonstrates the largest breakeven transaction cost buffer, indicating improved robustness to trading frictions.

Yaxuan Kong, Yoontae Hwang, Marcus Kaiser et al.

We introduce M2VN: Multi-Modal Volatility Network, a novel deep learning-based framework for financial volatility forecasting that unifies time series features with unstructured news data. M2VN leverages the representational power of deep neural networks to address two key challenges in this domain: (i) aligning and fusing heterogeneous data modalities, numerical financial data and textual information, and (ii) mitigating look-ahead bias that can undermine the validity of financial models. To achieve this, M2VN combines open-source market features with news embeddings generated by Time Machine GPT, a recently introduced point-in-time LLM, ensuring temporal integrity. An auxiliary alignment loss is introduced to enhance the integration of structured and unstructured data within the deep learning architecture. Extensive experiments demonstrate that M2VN consistently outperforms existing baselines, underscoring its practical value for risk management and financial decision-making in dynamic markets.

Yoontae Hwang, Stefan Zohren

Robust asset allocation is a key challenge in quantitative finance, where deep-learning forecasters often fail due to objective mismatch and error amplification. We introduce the Signature-Informed Transformer (SIT), a novel framework that learns end-to-end allocation policies by directly optimizing a risk-aware financial objective. SIT's core innovations include path signatures for a rich geometric representation of asset dynamics and a signature-augmented attention mechanism embedding financial inductive biases, like lead-lag effects, into the model. Evaluated on daily S\&P 100 equity data, SIT decisively outperforms traditional and deep-learning baselines, especially when compared to predict-then-optimize models. These results indicate that portfolio-aware objectives and geometry-aware inductive biases are essential for risk-aware capital allocation in machine-learning systems. The code is available at: https://github.com/Yoontae6719/Signature-Informed-Transformer-For-Asset-Allocation

Yaxuan Kong, Yiyuan Yang, Shiyu Wang et al.

Understanding time series data is crucial for multiple real-world applications. While large language models (LLMs) show promise in time series tasks, current approaches often rely on numerical data alone, overlooking the multimodal nature of time-dependent information, such as textual descriptions, visual data, and audio signals. Moreover, these methods underutilize LLMs' reasoning capabilities, limiting the analysis to surface-level interpretations instead of deeper temporal and multimodal reasoning. In this position paper, we argue that multimodal LLMs (MLLMs) can enable more powerful and flexible reasoning for time series analysis, enhancing decision-making and real-world applications. We call on researchers and practitioners to leverage this potential by developing strategies that prioritize trust, interpretability, and robust reasoning in MLLMs. Lastly, we highlight key research directions, including novel reasoning paradigms, architectural innovations, and domain-specific applications, to advance time series reasoning with MLLMs.

Yoontae Hwang, Yaxuan Kong, Stefan Zohren et al.

This paper addresses the critical disconnect between prediction and decision quality in portfolio optimization by integrating Large Language Models (LLMs) with decision-focused learning. We demonstrate both theoretically and empirically that minimizing the prediction error alone leads to suboptimal portfolio decisions. We aim to exploit the representational power of LLMs for investment decisions. An attention mechanism processes asset relationships, temporal dependencies, and macro variables, which are then directly integrated into a portfolio optimization layer. This enables the model to capture complex market dynamics and align predictions with the decision objectives. Extensive experiments on S\&P100 and DOW30 datasets show that our model consistently outperforms state-of-the-art deep learning models. In addition, gradient-based analyses show that our model prioritizes the assets most crucial to decision making, thus mitigating the effects of prediction errors on portfolio performance. These findings underscore the value of integrating decision objectives into predictions for more robust and context-aware portfolio management.

Felix Drinkall, Eghbal Rahimikia, Janet B. Pierrehumbert et al.

Large language models (LLMs) are often trained on extensive, temporally indiscriminate text corpora, reflecting the lack of datasets with temporal metadata. This approach is not aligned with the evolving nature of language. Conventional methods for creating temporally adapted language models often depend on further pre-training static models on time-specific data. This paper presents a new approach: a series of point-in-time LLMs called Time Machine GPT (TiMaGPT), specifically designed to be nonprognosticative. This ensures they remain uninformed about future factual information and linguistic changes. This strategy is beneficial for understanding language evolution and is of critical importance when applying models in dynamic contexts, such as time-series forecasting, where foresight of future information can prove problematic. We provide access to both the models and training datasets.

Peer Nagy, Sascha Frey, Kang Li et al.

While financial data presents one of the most challenging and interesting sequence modelling tasks due to high noise, heavy tails, and strategic interactions, progress in this area has been hindered by the lack of consensus on quantitative evaluation paradigms. To address this, we present LOB-Bench, a benchmark, implemented in python, designed to evaluate the quality and realism of generative message-by-order data for limit order books (LOB) in the LOBSTER format. Our framework measures distributional differences in conditional and unconditional statistics between generated and real LOB data, supporting flexible multivariate statistical evaluation. The benchmark also includes features commonly used LOB statistics such as spread, order book volumes, order imbalance, and message inter-arrival times, along with scores from a trained discriminator network. Lastly, LOB-Bench contains "market impact metrics", i.e. the cross-correlations and price response functions for specific events in the data. We benchmark generative autoregressive state-space models, a (C)GAN, as well as a parametric LOB model and find that the autoregressive GenAI approach beats traditional model classes.

Felix Drinkall, Janet B. Pierrehumbert, Stefan Zohren

Large language models (LLMs) have shown remarkable success in language modelling due to scaling laws found in model size and the hidden dimension of the model's text representation. Yet, we demonstrate that compressed representations of text can yield better performance in LLM-based regression tasks. In this paper, we compare the relative performance of embedding compression in three different signal-to-noise contexts: financial return prediction, writing quality assessment and review scoring. Our results show that compressing embeddings, in a minimally supervised manner using an autoencoder's hidden representation, can mitigate overfitting and improve performance on noisy tasks, such as financial return prediction; but that compression reduces performance on tasks that have high causal dependencies between the input and target data. Our results suggest that the success of interpretable compressed representations such as sentiment may be due to a regularising effect.

Felix Drinkall, Stefan Zohren, Michael McMahon et al.

Macroeconomic fluctuations and the narratives that shape them form a mutually reinforcing cycle: public discourse can spur behavioural changes leading to economic shifts, which then result in changes in the stories that propagate. We show that shifts in semantic embedding space can be causally linked to financial market shocks -- deviations from the expected market behaviour. Furthermore, we show how partisanship can influence the predictive power of text for market fluctuations and shape reactions to those same shocks. We also provide some evidence that text-based signals are particularly salient during unexpected events such as COVID-19, highlighting the value of language data as an exogenous variable in economic forecasting. Our findings underscore the bidirectional relationship between news outlets and market shocks, offering a novel empirical approach to studying their effect on each other.

Yuqi Nie, Yaxuan Kong, Xiaowen Dong et al.

Recent advances in large language models (LLMs) have unlocked novel opportunities for machine learning applications in the financial domain. These models have demonstrated remarkable capabilities in understanding context, processing vast amounts of data, and generating human-preferred contents. In this survey, we explore the application of LLMs on various financial tasks, focusing on their potential to transform traditional practices and drive innovation. We provide a discussion of the progress and advantages of LLMs in financial contexts, analyzing their advanced technologies as well as prospective capabilities in contextual understanding, transfer learning flexibility, complex emotion detection, etc. We then highlight this survey for categorizing the existing literature into key application areas, including linguistic tasks, sentiment analysis, financial time series, financial reasoning, agent-based modeling, and other applications. For each application area, we delve into specific methodologies, such as textual analysis, knowledge-based analysis, forecasting, data augmentation, planning, decision support, and simulations. Furthermore, a comprehensive collection of datasets, model assets, and useful codes associated with mainstream applications are presented as resources for the researchers and practitioners. Finally, we outline the challenges and opportunities for future research, particularly emphasizing a number of distinctive aspects in this field. We hope our work can help facilitate the adoption and further development of LLMs in the financial sector.

Yichi Zhang, Mihai Cucuringu, Alexander Y. Shestopaloff et al.

In multivariate time series systems, key insights can be obtained by discovering lead-lag relationships inherent in the data, which refer to the dependence between two time series shifted in time relative to one another, and which can be leveraged for the purposes of control, forecasting or clustering. We develop a clustering-driven methodology for robust detection of lead-lag relationships in lagged multi-factor models. Within our framework, the envisioned pipeline takes as input a set of time series, and creates an enlarged universe of extracted subsequence time series from each input time series, via a sliding window approach. This is then followed by an application of various clustering techniques, (such as k-means++ and spectral clustering), employing a variety of pairwise similarity measures, including nonlinear ones. Once the clusters have been extracted, lead-lag estimates across clusters are robustly aggregated to enhance the identification of the consistent relationships in the original universe. We establish connections to the multireference alignment problem for both the homogeneous and heterogeneous settings. Since multivariate time series are ubiquitous in a wide range of domains, we demonstrate that our method is not only able to robustly detect lead-lag relationships in financial markets, but can also yield insightful results when applied to an environmental data set.

Kieran Wood, Sven Giegerich, Stephen Roberts et al.

We introduce the Momentum Transformer, an attention-based deep-learning architecture, which outperforms benchmark time-series momentum and mean-reversion trading strategies. Unlike state-of-the-art Long Short-Term Memory (LSTM) architectures, which are sequential in nature and tailored to local processing, an attention mechanism provides our architecture with a direct connection to all previous time-steps. Our architecture, an attention-LSTM hybrid, enables us to learn longer-term dependencies, improves performance when considering returns net of transaction costs and naturally adapts to new market regimes, such as during the SARS-CoV-2 crisis. Via the introduction of multiple attention heads, we can capture concurrent regimes, or temporal dynamics, which are occurring at different timescales. The Momentum Transformer is inherently interpretable, providing us with greater insights into our deep-learning momentum trading strategy, including the importance of different factors over time and the past time-steps which are of the greatest significance to the model.

Eghbal Rahimikia, Stefan Zohren, Ser-Huang Poon

We examine whether news can improve realised volatility forecasting using a modern yet operationally simple NLP framework. News text is transformed into embedding-based representations, and forecasts are evaluated both as a standalone, news-only model and as a complement to standard realised volatility benchmarks. In out-of-sample tests on a cross-section of stocks, news contains useful predictive information, with stronger effects for stock-related content and during high volatility days. Combining the news-based signal with a leading benchmark yields consistent improvements in statistical performance and economically meaningful gains, while explainability analysis highlights the news themes most relevant for volatility.

Samuel Kessler, Jack Parker-Holder, Philip Ball et al.

Continual Learning (CL) considers the problem of training an agent sequentially on a set of tasks while seeking to retain performance on all previous tasks. A key challenge in CL is catastrophic forgetting, which arises when performance on a previously mastered task is reduced when learning a new task. While a variety of methods exist to combat forgetting, in some cases tasks are fundamentally incompatible with each other and thus cannot be learnt by a single policy. This can occur, in reinforcement learning (RL) when an agent may be rewarded for achieving different goals from the same observation. In this paper we formalize this "interference" as distinct from the problem of forgetting. We show that existing CL methods based on single neural network predictors with shared replay buffers fail in the presence of interference. Instead, we propose a simple method, OWL, to address this challenge. OWL learns a factorized policy, using shared feature extraction layers, but separate heads, each specializing on a new task. The separate heads in OWL are used to prevent interference. At test time, we formulate policy selection as a multi-armed bandit problem, and show it is possible to select the best policy for an unknown task using feedback from the environment. The use of bandit algorithms allows the OWL agent to constructively re-use different continually learnt policies at different times during an episode. We show in multiple RL environments that existing replay based CL methods fail, while OWL is able to achieve close to optimal performance when training sequentially.

Kieran Wood, Stephen Roberts, Stefan Zohren

Momentum strategies are an important part of alternative investments and are at the heart of commodity trading advisors (CTAs). These strategies have, however, been found to have difficulties adjusting to rapid changes in market conditions, such as during the 2020 market crash. In particular, immediately after momentum turning points, where a trend reverses from an uptrend (downtrend) to a downtrend (uptrend), time-series momentum (TSMOM) strategies are prone to making bad bets. To improve the response to regime change, we introduce a novel approach, where we insert an online changepoint detection (CPD) module into a Deep Momentum Network (DMN) [1904.04912] pipeline, which uses an LSTM deep-learning architecture to simultaneously learn both trend estimation and position sizing. Furthermore, our model is able to optimise the way in which it balances 1) a slow momentum strategy which exploits persisting trends, but does not overreact to localised price moves, and 2) a fast mean-reversion strategy regime by quickly flipping its position, then swapping it back again to exploit localised price moves. Our CPD module outputs a changepoint location and severity score, allowing our model to learn to respond to varying degrees of disequilibrium, or smaller and more localised changepoints, in a data driven manner. Back-testing our model over the period 1995-2020, the addition of the CPD module leads to an improvement in Sharpe ratio of one-third. The module is especially beneficial in periods of significant nonstationarity, and in particular, over the most recent years tested (2015-2020) the performance boost is approximately two-thirds. This is interesting as traditional momentum strategies have been underperforming in this period.

Zihao Zhang, Stefan Zohren

We design multi-horizon forecasting models for limit order book (LOB) data by using deep learning techniques. Unlike standard structures where a single prediction is made, we adopt encoder-decoder models with sequence-to-sequence and Attention mechanisms to generate a forecasting path. Our methods achieve comparable performance to state-of-art algorithms at short prediction horizons. Importantly, they outperform when generating predictions over long horizons by leveraging the multi-horizon setup. Given that encoder-decoder models rely on recurrent neural layers, they generally suffer from slow training processes. To remedy this, we experiment with utilising novel hardware, so-called Intelligent Processing Units (IPUs) produced by Graphcore. IPUs are specifically designed for machine intelligence workload with the aim to speed up the computation process. We show that in our setup this leads to significantly faster training times when compared to training models with GPUs.

Daniel Poh, Bryan Lim, Stefan Zohren et al.

The performance of a cross-sectional currency strategy depends crucially on accurately ranking instruments prior to portfolio construction. While this ranking step is traditionally performed using heuristics, or by sorting the outputs produced by pointwise regression or classification techniques, strategies using Learning to Rank algorithms have recently presented themselves as competitive and viable alternatives. Although the rankers at the core of these strategies are learned globally and improve ranking accuracy on average, they ignore the differences between the distributions of asset features over the times when the portfolio is rebalanced. This flaw renders them susceptible to producing sub-optimal rankings, possibly at important periods when accuracy is actually needed the most. For example, this might happen during critical risk-off episodes, which consequently exposes the portfolio to substantial, unwanted drawdowns. We tackle this shortcoming with an analogous idea from information retrieval: that a query's top retrieved documents or the local ranking context provide vital information about the query's own characteristics, which can then be used to refine the initial ranked list. In this work, we use a context-aware Learning-to-rank model that is based on the Transformer architecture to encode top/bottom ranked assets, learn the context and exploit this information to re-rank the initial results. Backtesting on a slate of 31 currencies, our proposed methodology increases the Sharpe ratio by around 30% and significantly enhances various performance metrics. Additionally, this approach also improves the Sharpe ratio when separately conditioning on normal and risk-off market states.

Zihao Zhang, Bryan Lim, Stefan Zohren

Market by order (MBO) data - a detailed feed of individual trade instructions for a given stock on an exchange - is arguably one of the most granular sources of microstructure information. While limit order books (LOBs) are implicitly derived from it, MBO data is largely neglected by current academic literature which focuses primarily on LOB modelling. In this paper, we demonstrate the utility of MBO data for forecasting high-frequency price movements, providing an orthogonal source of information to LOB snapshots and expanding the universe of alpha discovery. We provide the first predictive analysis on MBO data by carefully introducing the data structure and presenting a specific normalisation scheme to consider level information in order books and to allow model training with multiple instruments. Through forecasting experiments using deep neural networks, we show that while MBO-driven and LOB-driven models individually provide similar performance, ensembles of the two can lead to improvements in forecasting accuracy - indicating that MBO data is additive to LOB-based features.

Daniel Poh, Bryan Lim, Stefan Zohren et al.

The success of a cross-sectional systematic strategy depends critically on accurately ranking assets prior to portfolio construction. Contemporary techniques perform this ranking step either with simple heuristics or by sorting outputs from standard regression or classification models, which have been demonstrated to be sub-optimal for ranking in other domains (e.g. information retrieval). To address this deficiency, we propose a framework to enhance cross-sectional portfolios by incorporating learning-to-rank algorithms, which lead to improvements of ranking accuracy by learning pairwise and listwise structures across instruments. Using cross-sectional momentum as a demonstrative case study, we show that the use of modern machine learning ranking algorithms can substantially improve the trading performance of cross-sectional strategies -- providing approximately threefold boosting of Sharpe Ratios compared to traditional approaches.

Vincent Tan, Stefan Zohren

We introduce a novel covariance estimator for portfolio selection that adapts to the non-stationary or persistent heteroskedastic environments of financial time series by employing exponentially weighted averages and nonlinearly shrinking the sample eigenvalues through cross-validation. Our estimator is structure agnostic, transparent, and computationally feasible in large dimensions. By correcting the biases in the sample eigenvalues and aligning our estimator to more recent risk, we demonstrate that our estimator performs well in large dimensions against existing state-of-the-art static and dynamic covariance shrinkage estimators through simulations and with an empirical application in active portfolio management.

Diego Granziol, Stefan Zohren, Stephen Roberts

We study the effect of mini-batching on the loss landscape of deep neural networks using spiked, field-dependent random matrix theory. We demonstrate that the magnitude of the extremal values of the batch Hessian are larger than those of the empirical Hessian. We also derive similar results for the Generalised Gauss-Newton matrix approximation of the Hessian. As a consequence of our theorems we derive an analytical expressions for the maximal learning rates as a function of batch size, informing practical training regimens for both stochastic gradient descent (linear scaling) and adaptive algorithms, such as Adam (square root scaling), for smooth, non-convex deep neural networks. Whilst the linear scaling for stochastic gradient descent has been derived under more restrictive conditions, which we generalise, the square root scaling rule for adaptive optimisers is, to our knowledge, completely novel. %For stochastic second-order methods and adaptive methods, we derive that the minimal damping coefficient is proportional to the ratio of the learning rate to batch size. We validate our claims on the VGG/WideResNet architectures on the CIFAR-$100$ and ImageNet datasets. Based on our investigations of the sub-sampled Hessian we develop a stochastic Lanczos quadrature based on the fly learning rate and momentum learner, which avoids the need for expensive multiple evaluations for these key hyper-parameters and shows good preliminary results on the Pre-Residual Architecure for CIFAR-$100$.

Zihao Zhang, Stefan Zohren, Stephen Roberts

We adopt deep learning models to directly optimise the portfolio Sharpe ratio. The framework we present circumvents the requirements for forecasting expected returns and allows us to directly optimise portfolio weights by updating model parameters. Instead of selecting individual assets, we trade Exchange-Traded Funds (ETFs) of market indices to form a portfolio. Indices of different asset classes show robust correlations and trading them substantially reduces the spectrum of available assets to choose from. We compare our method with a wide range of algorithms with results showing that our model obtains the best performance over the testing period, from 2011 to the end of April 2020, including the financial instabilities of the first quarter of 2020. A sensitivity analysis is included to understand the relevance of input features and we further study the performance of our approach under different cost rates and different risk levels via volatility scaling.

Bryan Lim, Stefan Zohren

Numerous deep learning architectures have been developed to accommodate the diversity of time series datasets across different domains. In this article, we survey common encoder and decoder designs used in both one-step-ahead and multi-horizon time series forecasting -- describing how temporal information is incorporated into predictions by each model. Next, we highlight recent developments in hybrid deep learning models, which combine well-studied statistical models with neural network components to improve pure methods in either category. Lastly, we outline some ways in which deep learning can also facilitate decision support with time series data.

Bryan Lim, Stefan Zohren, Stephen Roberts

Detecting changes in asset co-movements is of much importance to financial practitioners, with numerous risk management benefits arising from the timely detection of breakdowns in historical correlations. In this article, we propose a real-time indicator to detect temporary increases in asset co-movements, the Autoencoder Reconstruction Ratio, which measures how well a basket of asset returns can be modelled using a lower-dimensional set of latent variables. The ARR uses a deep sparse denoising autoencoder to perform the dimensionality reduction on the returns vector, which replaces the PCA approach of the standard Absorption Ratio, and provides a better model for non-Gaussian returns. Through a systemic risk application on forecasting on the CRSP US Total Market Index, we show that lower ARR values coincide with higher volatility and larger drawdowns, indicating that increased asset co-movement does correspond with periods of market weakness. We also demonstrate that short-term (i.e. 5-min and 1-hour) predictors for realised volatility and market crashes can be improved by including additional ARR inputs.

Diego Granziol, Robin Ru, Stefan Zohren et al.

Graph spectral techniques for measuring graph similarity, or for learning the cluster number, require kernel smoothing. The choice of kernel function and bandwidth are typically chosen in an ad-hoc manner and heavily affect the resulting output. We prove that kernel smoothing biases the moments of the spectral density. We propose an information theoretically optimal approach to learn a smooth graph spectral density, which fully respects the moment information. Our method's computational cost is linear in the number of edges, and hence can be applied to large networks, with millions of nodes. We apply our method to the problems to graph similarity and cluster number learning, where we outperform comparable iterative spectral approaches on synthetic and real graphs.

Samuel Kessler, Vu Nguyen, Stefan Zohren et al.

We place an Indian Buffet process (IBP) prior over the structure of a Bayesian Neural Network (BNN), thus allowing the complexity of the BNN to increase and decrease automatically. We further extend this model such that the prior on the structure of each hidden layer is shared globally across all layers, using a Hierarchical-IBP (H-IBP). We apply this model to the problem of resource allocation in Continual Learning (CL) where new tasks occur and the network requires extra resources. Our model uses online variational inference with reparameterisation of the Bernoulli and Beta distributions, which constitute the IBP and H-IBP priors. As we automatically learn the number of weights in each layer of the BNN, overfitting and underfitting problems are largely overcome. We show empirically that our approach offers a competitive edge over existing methods in CL.

Zihao Zhang, Stefan Zohren, Stephen Roberts

We adopt Deep Reinforcement Learning algorithms to design trading strategies for continuous futures contracts. Both discrete and continuous action spaces are considered and volatility scaling is incorporated to create reward functions which scale trade positions based on market volatility. We test our algorithms on the 50 most liquid futures contracts from 2011 to 2019, and investigate how performance varies across different asset classes including commodities, equity indices, fixed income and FX markets. We compare our algorithms against classical time series momentum strategies, and show that our method outperforms such baseline models, delivering positive profits despite heavy transaction costs. The experiments show that the proposed algorithms can follow large market trends without changing positions and can also scale down, or hold, through consolidation periods.

Diego Granziol, Binxin Ru, Stefan Zohren et al.

Efficient approximation lies at the heart of large-scale machine learning problems. In this paper, we propose a novel, robust maximum entropy algorithm, which is capable of dealing with hundreds of moments and allows for computationally efficient approximations. We showcase the usefulness of the proposed method, its equivalence to constrained Bayesian variational inference and demonstrate its superiority over existing approaches in two applications, namely, fast log determinant estimation and information-theoretic Bayesian optimisation.

Bryan Lim, Stefan Zohren, Stephen Roberts

Despite recent innovations in network architectures and loss functions, training RNNs to learn long-term dependencies remains difficult due to challenges with gradient-based optimisation methods. Inspired by the success of Deep Neuroevolution in reinforcement learning (Such et al. 2017), we explore the use of gradient-free population-based global optimisation (PBO) techniques -- training RNNs to capture long-term dependencies in time-series data. Testing evolution strategies (ES) and particle swarm optimisation (PSO) on an application in volatility forecasting, we demonstrate that PBO methods lead to performance improvements in general, with ES exhibiting the most consistent results across a variety of architectures.