Comparative Evaluation of LSTM, TCN, and Quantile Regression with Conformal Prediction for Time Series Forecasting under Uncertainty

Accurate forecasting with uncertainty quantification is essential in high-risk time series applications. Conformal Prediction (CP) offers a model-agnostic way to generate valid prediction intervals. This paper compares three forecasting models-LSTM, TCN, and Quantile Regression-combined with Split CP for uncertainty-aware prediction. Experiments on three real-world datasets-S&P 500 (finance), PM2.5 (environment), and total phosphorus in wastewater (industrial control)-highlight key trade-offs. CQR achieves the best coverage but with wide intervals and lower accuracy. LSTM offers sharper predictions but suffers from under-coverage. TCN provides a balanced performance across most tasks. We evaluate empirical coverage, interval width, prediction accuracy, and calibration curves. Results show that model choice depends on domain-specific needs: accuracy, reliability, or robustness. This work offers practical guidance for applying CP-based forecasting and is, to our knowledge, the first to benchmark LSTM, TCN, and QR under a unified conformal framework across multiple domains.