Paper: arXiv 2410.18897

Abstract

Despite its practical significance, generating realistic synthetic financial time series is challenging due to statistical properties known as stylized facts, such as fat tails, volatility clustering, and seasonality patterns. Various generative models, including generative adversarial networks (GANs) and variational autoencoders (VAEs), have been employed to address this challenge, although no model yet satisfies all the stylized facts. We alternatively propose utilizing diffusion models, specifically denoising diffusion probabilistic models (DDPMs), to generate synthetic financial time series. This approach employs wavelet transformation to convert multiple time series (into images), such as stock prices, trading volumes, and spreads. Given these converted images, the model gains the ability to generate images that can be transformed back into realistic time series by inverse wavelet transformation. We demonstrate that our proposed approach satisfies stylized facts.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 5.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematical concepts like diffusion models and wavelet transformations, indicating high complexity, while demonstrating the approach with concrete experimental setups and stylized fact reproduction, showing significant empirical rigor.

Research Flowchart

  flowchart TD
  A["Research Goal: Generate realistic synthetic<br/>financial time series"] --> B["Input: Real Financial Data<br/>(Prices, Volumes, Spreads)"]
  B --> C["Wavelet Transform: Convert time series to images"]
  C --> D["Diffusion Model DDPM Training<br/>on converted images"]
  D --> E["Model Generation: Create synthetic images"]
  E --> F["Inverse Wavelet Transform: Convert back to time series"]
  F --> G["Outcome: Validated synthetic data<br/>Satisfies stylized facts"]