NQF-RNN: probabilistic forecasting via neural quantile function-based recurrent neural networks

Probabilistic forecasting offers insights beyond point estimates, supporting more informed decision-making. This paper introduces the Neural Quantile Function with Recurrent Neural Networks (NQF-RNN), a model for multistep-ahead probabilistic time series forecasting. NQF-RNN combines neural quantile functions with recurrent neural networks, enabling applicability across diverse time series datasets. The model uses a monotonically increasing neural quantile function and is trained with a continuous ranked probability score (CRPS)-based loss function. NQF-RNN’s performance is evaluated on synthetic datasets generated from multiple distributions and six real-world time series datasets with both periodicity and irregularities. NQF-RNN demonstrates competitive performance on synthetic data and outperforms benchmarks on real-world data, achieving lower average forecast errors across most metrics. Notably, NQF-RNN surpasses benchmarks in CRPS, a key probabilistic metric, and tail-weighted CRPS, which assesses tail event forecasting with a narrow prediction interval. The model outperforms other deep learning models by 5% to 41% in CRPS, with improvements of 5% to 53% in left tail-weighted CRPS and 6% to 34% in right tail-weighted CRPS. Against its baseline model, DeepAR, NQF-RNN achieves a 41% improvement in CRPS, indicating its effectiveness in generating reliable prediction intervals. These results highlight NQF-RNN’s robustness in managing complex and irregular patterns in real-world forecasting scenarios.