  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.
