# Time-Causal VAE: Robust Financial Time Series Generator

arXiv: https://arxiv.org/abs/2411.02947 · HTML: https://mlsanity.com/paper/2411.02947/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 103 references that are in the map.
- First posted on arXiv 5 Nov 2024.

## Builds on (most cited first, 30 of 46)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Images](https://mlsanity.com/paper/2011.10650/) (2020)
- [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1611.02648/) (2016)
- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [Variational Lossy Autoencoder](https://mlsanity.com/paper/1611.02731/) (2016)
- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generation](https://mlsanity.com/paper/2111.08095/) (2021)
- [Dynamical Variational Autoencoders: A Comprehensive Review](https://mlsanity.com/paper/2008.12595/) (2020)
- [Machine Learning for Synthetic Data Generation: A Review](https://mlsanity.com/paper/2302.04062/) (2023)
- [Max-Sliced Wasserstein Distance and its use for GANs](https://mlsanity.com/paper/1904.05877/) (2019)
- [Causal Attention for Vision-Language Tasks](https://mlsanity.com/paper/2103.03493/) (2021)
- [Quant GANs: Deep Generation of Financial Time Series](https://mlsanity.com/paper/1907.06673/) (2019)
- [Taming VAEs](https://mlsanity.com/paper/1810.00597/) (2018)
- [COT-GAN: Generating Sequential Data via Causal Optimal Transport](https://mlsanity.com/paper/2006.08571/) (2020)
- [Sig-Wasserstein GANs for Time Series Generation](https://mlsanity.com/paper/2111.01207/) (2021)
- [Signature moments to characterize laws of stochastic processes](https://mlsanity.com/paper/1810.10971/) (2018)
- [Data Augmentation techniques in time series domain: A survey and taxonomy](https://mlsanity.com/paper/2206.13508/) (2022)
- [Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distances](https://mlsanity.com/paper/2210.09160/) (2022)
- [Non-adversarial training of Neural SDEs with signature kernel scores](https://mlsanity.com/paper/2305.16274/) (2023)
- [A Data-driven Market Simulator for Small Data Environments](https://mlsanity.com/paper/2006.14498/) (2020)
- [Wasserstein GANs Work Because They Fail (to Approximate the Wasserstein Distance)](https://mlsanity.com/paper/2103.01678/) (2021)
- [Generating Realistic Stock Market Order Streams](https://mlsanity.com/paper/2006.04212/) (2020)
- [Towards Realistic Market Simulations: a Generative Adversarial Networks Approach](https://mlsanity.com/paper/2110.13287/) (2021)
- [Conditional Sig-Wasserstein GANs for Time Series Generation](https://mlsanity.com/paper/2006.05421/) (2020)

## Built on by (most cited first, 8 of 8)

- [Schr"odinger bridge for generative AI: Soft-constrained formulation and convergence analysis](https://mlsanity.com/paper/2510.11829/) (2025)
- [Towards Causal Market Simulators](https://mlsanity.com/paper/2511.04469/) (2025)
- [Diffusion Models for Adaptive Sequential Data Generation](https://mlsanity.com/paper/2606.06007/) (2026)
- [Towards Time Series Generation Conditioned on Unstructured Natural Language](https://mlsanity.com/paper/2506.22927/) (2025)
- [Nested Optimal Transport Distances](https://mlsanity.com/paper/2509.06702/) (2025)
- [From Vessel Trajectories to Safety-Critical Encounter Scenarios: A Generative AI Framework for Autonomous Ship Digital Testing](https://mlsanity.com/paper/2603.28067/) (2026)
- [Efficient Learning of Deep State Space Models via Importance Smoothing](https://mlsanity.com/paper/2605.21108/) (2026)
- [UPLOTS: A Unified Pretrained Language Model for Constrained Time-series Generation](https://mlsanity.com/paper/2606.10466/) (2026)

## Abstract (arXiv)

We build a time-causal variational autoencoder (TC-VAE) for robust generation of financial time series data. Our approach imposes a causality constraint on the encoder and decoder networks, ensuring a causal transport from the real market time series to the fake generated time series. Specifically, we prove that the TC-VAE loss provides an upper bound on the causal Wasserstein distance between market distributions and generated distributions. Consequently, the TC-VAE loss controls the discrepancy between optimal values of various dynamic stochastic optimization problems under real and generated distributions. To further enhance the model's ability to approximate the latent representation of the real market distribution, we integrate a RealNVP prior into the TC-VAE framework. Finally, extensive numerical experiments show that TC-VAE achieves promising results on both synthetic and real market data. This is done by comparing real and generated distributions according to various statistical distances, demonstrating the effectiveness of the generated data for downstream financial optimization tasks, as well as showcasing that the generated data reproduces stylized facts of real financial market data.