Generation of synthetic financial time series by diffusion models

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.