Paper: arXiv 2603.01820

Authors: Adir Saly-Kaufmann, Kieran Wood, Jan Peter-Calliess, Stefan Zohren

Abstract

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.

Complexity vs Empirical Score

  • Math Complexity: 4.5/10
  • Empirical Rigor: 6.0/10 (capped from 8.5: transaction costs only partially modelled; see penalty flags)
  • Quadrant: Street Traders — practical and empirical, lighter on theory

Why this score: This paper presents an exceptionally thorough benchmark of deep learning architectures applied to portfolio optimization across multiple asset classes over a 15-year dataset. While the underlying mathematical formulations are relatively standard, the empirical rigor—including breakeven transaction cost analysis, downside risk measures, and seed robustness—is outstanding.

Research Flowchart

  flowchart TD
    A[Goal: Benchmark Deep Learning Models for Financial Time Series & Position Sizing] --> B[Data: Daily Futures 2010–2025<br/>Commodities, Equities, Bonds, FX]
    B --> C[Tested Models: Linear, Recurrent, Transformers,<br/>State Space Models & Hybrids]
    C --> D[Optimization & Evaluation:<br/>Sharpe Ratio, Downside Risk, Costs & Efficiency]
    D --> E1[Highest Overall Sharpe:<br/>VSN + LSTM]
    D --> E2[Best Downside Risk:<br/>VSN + xLSTM & PatchTST + LSTM]
    D --> E3[Highest Transaction Cost Buffer:<br/>xLSTM]

Cited References (49)

  1. Pinnacle Data Corp. CLC Database — link
  2. Attention Is All You Need (2017)
  3. A Comprehensive Survey on Applications of Transformers for Deep Learning Tasks (2024) — link
  4. iTransformer : Inverted Transformers Are Effective for Time Series Forecasting (2024) — link
  5. A Time Series is Worth 64 Words: Long-term Forecasting with Transformers (2023) — link
  6. Trading with the Momentum Transformer: An Intelligent and Interpretable Architecture (2021) — link
  7. Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting (2021) — link
  8. Mamba: Linear-Time Sequence Modeling with Selective State Spaces (2024) — link
and 41 more
  1. Transformers are SSMs : Generalized Models and Efficient Algorithms through Structured State Space Duality (2024) — link
  2. HiPPO : Recurrent Memory with Optimal Polynomial Projections (2020) — link
  3. Were RNN s All We Needed? (2024) — link
  4. Recurrent Neural Networks for Time Series Forecasting: Current Status and Future Directions (2021) — link
  5. Long Short-Term Memory (1997) — link
  6. xLSTM : Extended Long Short-Term Memory (2024) — link
  7. Unlocking the Power of LSTM for Long Term Time Series Forecasting (2025) — link
  8. Deep Time Series Models: A Comprehensive Survey and Benchmark (2024) — link
  9. Are Transformers Effective for Time Series Forecasting? (2023) — link
  10. Empirical Properties of Asset Returns: Stylized Facts and Statistical Issues (2001) — link
  11. Performance Evaluation of Deep Neural Networks for Forecasting Time-Series with Multiple Structural Breaks and High Volatility (2019) — link
  12. On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer’s Sunspot Numbers (1927) — link
  13. Transformers are RNN s: Fast Autoregressive Transformers with Linear Attention (2020) — link
  14. Financial Time Series Forecasting with Deep Learning: A Systematic Literature Review: 2005–2019 (2019) — link
  15. Deep Time Series Forecasting Models: A Comprehensive Survey (2024) — link
  16. Financial Time Series Models—Comprehensive Review of Deep Learning Approaches and Practical Recommendations (2023) — link
  17. Why Do Transformers Fail to Forecast Time Series In-Context? (2025) — link
  18. Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting (2022) — link
  19. Evaluating the Effectiveness of Time Series Transformers for Demand Forecasting (2024) — link
  20. Efficiently Modeling Long Sequences with Structured State Spaces (2022) — link
  21. Long Short-Term Memory Neural Network for Financial Time Series (2022) — link
  22. Time-Series Forecasting with Deep Learning: A Survey (2021) — link
  23. LSTM Networks for Data-Driven Forecasting of Noisy Time Series (2019)
  24. Deep Learning Models for Price Forecasting of Financial Time Series: A Review of Recent Advancements (2020–2022) (2023) — link
  25. Realized Volatility Forecasting with Neural Networks (2020) — link
  26. Correlation Matrix Memories (1972) — link
  27. A Simple Neural Network Generating an Interactive Memory (1972) — link
  28. Associatron—A Model of Associative Memory (1972) — link
  29. Distinctive Features, Categorical Perception, and Probability Learning: Some Applications of a Neural Model (1977) — link
  30. Few-Shot Learning Patterns in Financial Time Series for Trend-Following Strategies — → 2310.10500
  31. DeePM : Regime-Robust Deep Learning for Systematic Macro Portfolio Management (2026) — link
  32. Enhancing Time-Series Momentum Strategies Using Deep Neural Networks (2019) — link
  33. Time Series Momentum (2012) — link
  34. The Impact of Volatility Targeting (2018) — link
  35. Contrastive Learning of Asset Embeddings from Financial Time Series (2024) — link
  36. Entity embeddings of categorical variables (2016) — link
  37. Modern Portfolio Theory and Investment Analysis (2014)
  38. The Sharpe Ratio (1994)
  39. A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix (1987)
  40. A Simple Nonparametric Test of Predictive Performance (1992)
  41. Adam: A Method for Stochastic Optimization (2015)

1 of 49 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.