ReLU DNNs get prediction intervals for reliable time series forecasting
New method quantifies both future variability and training estimation uncertainty in deep learning forecasts.
Kejin Wu's new paper tackles a critical gap in deep learning time series forecasting: uncertainty quantification. While neural networks excel at prediction due to their universal approximation abilities, their predictive uncertainty is often poorly studied. The proposed methodology builds Pertinent Prediction Intervals (PPI) using standard ReLU DNN estimators, explicitly separating two sources of uncertainty: variability in future observations and estimation uncertainty within the training data. This dual decomposition is crucial for reliable interval coverage.
The theoretical framework is rigorous. Wu first proves the consistency of the ReLU DNN estimator under beta-mixing dependent data, a common assumption for time series. Then he demonstrates that the implied forward bootstrap series remains beta-mixing and shares the same stationary distribution as the original series in probability—a key condition for the PPI to work. Finally, minimal conditions on the limiting distribution of predictive roots complete the interval construction. Simulations and real-data experiments show the PPI approach compares favorably against standard non-parametric methods, suggesting DNN-based intervals can be both robust and practical.
- Introduces Pertinent Prediction Intervals (PPI) for standard ReLU DNN time series models, capturing both future and estimation uncertainty.
- Proves DNN estimator consistency under beta-mixing dependent data, a key property for dependent time series observations.
- Demonstrates the bootstrap series preserves stationarity, validated via simulations and real-data benchmarks against non-parametric methods.
Why It Matters
Gives data scientists a rigorous way to trust deep learning time series forecasts with statistically valid confidence intervals.