High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes

TL;DR

This paper introduces a scalable method combining RNNs and low-rank Gaussian copula processes to model high-dimensional, non-Gaussian multivariate time series, improving accuracy in real-world applications.

Contribution

It presents a novel approach that reduces computational complexity, enabling modeling of thousands of time series with time-varying dependencies, surpassing existing methods.

Findings

Significant accuracy improvements over state-of-the-art baselines.

Effective modeling of dependencies in high-dimensional datasets.

Ablation study confirming the contributions of each model component.

Abstract

Predicting the dependencies between observations from multiple time series is critical for applications such as anomaly detection, financial risk management, causal analysis, or demand forecasting. However, the computational and numerical difficulties of estimating time-varying and high-dimensional covariance matrices often limits existing methods to handling at most a few hundred dimensions or requires making strong assumptions on the dependence between series. We propose to combine an RNN-based time series model with a Gaussian copula process output model with a low-rank covariance structure to reduce the computational complexity and handle non-Gaussian marginal distributions. This permits to drastically reduce the number of parameters and consequently allows the modeling of time-varying correlations of thousands of time series. We show on several real-world datasets that our method provides significant accuracy improvements over state-of-the-art baselines and perform an ablation study analyzing the contributions of the different components of our model.