Paper: arXiv 2407.19848

Authors: Chung I Lu, Julian Sester

Abstract

Generating synthetic financial time series data that accurately reflects real-world market dynamics holds tremendous potential for various applications, including portfolio optimization, risk management, and large scale machine learning. We present an approach that {uses structured noise} for training generative models for financial time series. The expressive power of the signature transform {has been shown to be able} to capture the complex dependencies and temporal structures inherent in financial data {when used to train generative models in the form of a signature kernel }. We employ a moving average model to model the variance of the noise input, enhancing the model’s ability to reproduce stylized facts such as volatility clustering. Through empirical experiments on S&P 500 index data, we demonstrate that our model effectively captures key characteristics of financial time series and outperforms comparable {approaches}. In addition, we explore the application of the synthetic data generated to train a reinforcement learning agent for portfolio management, achieving promising results. Finally, we propose a method to add robustness to the generative model by tweaking the noise input so that the generated sequences can be adjusted to different market environments with minimal data.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.0/10 (capped from 7.5: transaction costs not modelled; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper combines sophisticated mathematical tools like MMD and signature kernels with a practical GARCH-like moving average noise structure to generate financial time series. The empirical evaluation is strong, featuring comparisons against existing benchmarks (COT-GAN, Sig-WGAN) and a downstream reinforcement learning application for portfolio management.

Research Flowchart

  flowchart TD
    A["Research Goal: Generate realistic financial time series capturing stylized facts"] --> B["Data Input: S&P 500 Index Data"]
    B --> C["Model Design: Generative Model with Structured Noise & Moving Average Variance"]
    C --> D["Training: MMD-based Signature Kernel Learning"]
    D --> E["Evaluation & Application: RL Portfolio Management & Robustness Tweaking"]
    E --> F["Outcomes: Superior capture of volatility clustering & adaptivity to market environments"]

Cited References (58)

  1. Time-Causal VAE: Robust Financial Time Series Generator — → 2411.02947
  2. Universal randomised signatures for generative time series modelling — → 2406.10214
  3. Evaluation of Deep Reinforcement Learning Algorithms for Portfolio Optimisation — → 2307.07694
  4. Non-adversarial training of Neural SDEs with signature kernel scores — → 2305.16274
  5. Simulating financial time series using attention (2022) — link
  6. Signature Methods in Machine Learning (2022) — link
  7. Diverse Weight Averaging for Out-of-Distribution Generalization (2022) — link
  8. Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time (2022) — link
and 50 more
  1. T ail -GAN: Learning to Simulate Tail Risk Scenarios (2022) — link
  2. On Neural Differential Equations (2022) — link
  3. On the effectiveness of Randomized Signatures as Reservoir for Learning Rough Dynamics (2022) — link
  4. Multi-Asset Spot and Option Market Simulation (2021) — link
  5. Sig-wasserstein GANs for time series generation (2021) — link
  6. Towards realistic market simulations: a generative adversarial networks approach (2021) — link
  7. Neural SDEs as Infinite-Dimensional GANs (2021) — link
  8. Generating synthetic data in finance: opportunities, challenges and pitfalls (2020) — link
  9. DiffWave: A Versatile Diffusion Model for Audio Synthesis (2020) — link
  10. The Signature Kernel Is the Solution of a Goursat PDE (2020) — link
  11. A Data-driven Market Simulator for Small Data Environments (2020) — link
  12. Denoising Diffusion Probabilistic Models (2020) — link
  13. COT-GAN: Generating Sequential Data via Causal Optimal Transport (2020) — link
  14. Sig‐Wasserstein GANs for conditional time series generation (2020) — link
  15. Estimating processes in adapted Wasserstein distance (2020) — link
  16. Embedding and learning with signatures (2019) — link
  17. Modeling financial time-series with generative adversarial networks (2019) — link
  18. Quant GANs: deep generation of financial time series (2019) — link
  19. Generative Modeling by Estimating Gradients of the Data Distribution (2019) — link
  20. Unbiased estimators for the variance of MMD estimators (2019) — link
  21. The Market Generator (2019) — link
  22. Generative adversarial networks for financial trading strategies fine-tuning and combination (2019) — link
  23. Signature Moments to Characterize Laws of Stochastic Processes (2018) — link
  24. Demystifying MMD GANs (2018) — link
  25. Proximal Policy Optimization Algorithms (2017) — link
  26. Wasserstein Generative Adversarial Networks (2017)
  27. Kernel Mean Embedding of Distributions: A Review and Beyonds (2016) — link
  28. A Primer on the Signature Method in Machine Learning (2016) — link
  29. Kernels for sequentially ordered data (2016) — link
  30. The Lambert Way to Gaussianize Heavy-Tailed Data with the Inverse of Tukey’s h Transformation as a Special Case (2015) — link
  31. Inverting the signature of a path (2014) — link
  32. Rough paths, Signatures and the modelling of functions on streams (2014) — link
  33. Estimate nothing (2014) — link
  34. Auto-Encoding Variational Bayes (2013) — link
  35. Release (2012) — link
  36. A Kernel Two-Sample Test (2012) — link
  37. Universality, Characteristic Kernels and RKHS Embedding of Measures (2010) — link
  38. Support Vector Machines (2008) — link
  39. Uniqueness for the signature of a path of bounded variation and the reduced path group (2005) — link
  40. Empirical properties of asset returns: stylized facts and statistical issues (2001) — link
  41. Long Short-Term Memory (1997) — link
  42. A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options (1993) — link
  43. Generative Learning for Financial Time Series with Irregular and Scale-Invariant Patterns (2024)
  44. Neural stochastic differential equations for conditional time series generation using the Signature-Wasserstein-1 metric (2023) — link
  45. Time-series Generative Adversarial Networks (2019)
  46. GENERATIVE ADVERSARIAL NETS (2018)
  47. Deep Learning (2016) — link
  48. Differential equations driven by rough paths (2007) — link
  49. Gaussian processes for machine learning , volume 2 (2006)
  50. Market efficiency before and after the introduction of electronic trading at the Toronto stock exchange (1997) — link

4 of 58 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.