35: Time Series Forecasting with Conformal Prediction: A Critical Assessment

Music City Center 

Forecasting time series is critical in domains like finance, epidemiology, and engineering. Classical models like ARIMA, GARCH, and state-space formulations capture temporal dependencies and volatility structures, while modern approaches like reservoir computing and deep learning handle complex dynamics. A key challenge across these methods is principled uncertainty quantification. Conformal prediction (CP) provides a model-agnostic framework for constructing prediction intervals with finite-sample validity, ensuring reliable uncertainty quantification. However, CP's efficiency varies across data-generating processes (DGPs), particularly in settings with residual dependence, complex temporal structures, or limited data.

This study evaluates CP across diverse DGPs, including stationary and non-stationary processes, latent-state models, and differential equation-driven systems. We compare classical and modern forecasting methods on interval coverage, efficiency, and robustness under distribution shifts. Additionally, we explore empirical Bayes as a bridge between likelihood-based inference and CP, offering insights into balancing predictive flexibility and reliability.

Conformal Prediction

Time Series Forecasting

Uncertainty Quantification

Machine Learning 

Section on Statistical Computing