🤖 AI Summary
This study addresses the challenge of modeling predictive distributions for nonlinear, multivariate time series by proposing a general generative representation framework grounded in measure-theoretic probability, which is, to the authors’ knowledge, the first to be integrated with conditional generative adversarial networks (CGANs). Under a mild temporal dependence assumption, the method establishes estimation consistency in the Hausdorff metric and enables efficient simulation and computation of conditional means, variances, and risk measures. Empirical results demonstrate that the model achieves strong predictive performance on tasks involving stock returns, realized variances, and covariances, delivering high accuracy with remarkable computational efficiency—requiring only about one minute for a single training run.
📝 Abstract
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.