Accurate uncertainty measurement is a key step in building robust and reliable machine learning systems. Conformal prediction is a distribution-free uncertainty quantification framework popular for its ease of implementation, finite-sample coverage guarantees, and generality for underlying prediction algorithms. However, existing conformal prediction approaches for time series are limited to single-step prediction without considering the temporal dependency. In this paper, we propose the Copula Conformal Prediction algorithm for multivariate, multi-step Time Series forecasting, CopulaCPTS. We prove that CopulaCPTS has finite-sample validity guarantee. On four synthetic and real-world multivariate time series datasets, we show that CopulaCPTS produces more calibrated and efficient confidence intervals for multi-step prediction tasks than existing techniques. Our code is open-sourced at https://github.com/Rose-STL-Lab/CopulaCPTS.

Selecting appropriate thresholds for anomaly detection in online, unsupervised settings is a challenging task, especially in the presence of data distribution shifts. Addressing these challenges is critical in many practical large scale systems, such as infrastructure monitoring and network intrusion detection. This paper proposes an algorithm that connects online thresholding with constructing confidence sequences achieving (1) adaptive online threshold selection robust to distribution shifts, (2) statistical guarantees on false positive and false negative rates without any distributional assumptions, and (3) improved performance when given relevant offline data to warm-start the online algorithm, while having bounded degradation if the offline data is irrelevant. We complement our theoretical results by empirical evidence that our method outperforms commonly used baselines across synthetic and real world datasets.