# Generative Predictive Distributions for Time Series

arXiv: https://arxiv.org/abs/2606.16773 · HTML: https://mlsanity.com/paper/2606.16773/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 76 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks](https://mlsanity.com/paper/1703.02930/) (2017)
- [The relativistic discriminator: a key element missing from standard GAN](https://mlsanity.com/paper/1807.00734/) (2018)
- [Deep Network Approximation Characterized by Number of Neurons](https://mlsanity.com/paper/1906.05497/) (2019)
- [Quant GANs: Deep Generation of Financial Time Series](https://mlsanity.com/paper/1907.06673/) (2019)
- [Efficient Methods for Structured Nonconvex-Nonconcave Min-Max Optimization](https://mlsanity.com/paper/2011.00364/) (2020)
- [The GAN is dead; long live the GAN! A Modern GAN Baseline](https://mlsanity.com/paper/2501.05441/) (2025)
- [Deep Learning in Asset Pricing](https://mlsanity.com/paper/1904.00745/) (2019)
- [Conditional Density Estimation with Neural Networks: Best Practices and Benchmarks](https://mlsanity.com/paper/1903.00954/) (2019)
- [Using Wasserstein Generative Adversarial Networks for the Design of Monte Carlo Simulations](https://mlsanity.com/paper/1909.02210/) (2019)
- [Some Theoretical Properties of GANs](https://mlsanity.com/paper/1803.07819/) (2018)
- [Nonparametric Conditional Density Estimation in a High-Dimensional Regression Setting](https://mlsanity.com/paper/1604.00540/) (2016)
- [Two-Timescale Gradient Descent Ascent Algorithms for Nonconvex Minimax Optimization](https://mlsanity.com/paper/2408.11974/) (2024)
- [Rates of convergence for density estimation with generative adversarial networks](https://mlsanity.com/paper/2102.00199/) (2021)
- [Nonsmooth Nonconvex-Nonconcave Minimax Optimization: Primal-Dual Balancing and Iteration Complexity Analysis](https://mlsanity.com/paper/2209.10825/) (2022)
- [Wasserstein Generative Regression](https://mlsanity.com/paper/2306.15163/) (2023)
- [On Relativistic f-Divergences](https://mlsanity.com/paper/1901.02474/) (2019)
- [An Adversarial Approach to Structural Estimation](https://mlsanity.com/paper/2007.06169/) (2020)
- [Time Series (re)sampling using Generative Adversarial Networks](https://mlsanity.com/paper/2102.00208/) (2021)
- [Statistical analysis of Wasserstein GANs with applications to time series forecasting](https://mlsanity.com/paper/2011.03074/) (2020)
- [Statistical inference for generative adversarial networks and other minimax problems](https://mlsanity.com/paper/2104.10601/) (2021)

## Abstract (arXiv)

We propose a flexible framework for modeling the predictive distributions of nonlinear, possibly multivariate time series. Our approach expresses a general predictive distribution in an appropriate generative representation that is based on a folklore result from measure theoretic probability. This representation provides a direct simulation-based approximation to the predictive distribution, enabling straightforward computation of forecasts for the conditional mean and variance, fan charts, value at risk, expected shortfall, joint tail risks, and other quantities of interest. We estimate this generative representation using a version of conditional generative adversarial networks and provide a formal statistical analysis of estimation under weak temporal dependence. Specifically, estimation is expressed as a particular minimax problem and we establish consistency of its approximate solutions in Hausdorff distance. The empirical relevance of the approach is illustrated using applications to equity returns, realized variance, and realized covariances. The proposed method is also computationally manageable, with estimation in our applications taking approximately one minute on a standard laptop.