Uncertainty Quantification and Its Improvement in Machine Learning Using GARCH and DBPS for Time Series Forecasting

Abstract

This study proposes a novel approach to improve forecast accuracy and uncertainty quantification in time series forecasting through the synthesis of Machine Learning (ML) models with Dynamic Bayesian Predictive Synthesis (DBPS). We synthesize predictive distributions from three ML models—LightGBM, LSTM, and Prophet—through DBPS, notably employing Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models to estimate uncertainties for ML forecasts. Empirical analysis using meteorological data from Delhi, India, demonstrates that our proposed method outperforms individual ML models and conventional ensemble methods, achieving improvements of up to 25.2% in RMSE and 25.4% in MAE. Furthermore, evaluating predictive distributions using Log Predictive Density Ratio (LPDR) reveals superior performance to other models, indicating a more accurate capture of observational uncertainty. Analysis of DBPS weights reveals that the offsetting effect of prediction biases is one of the factors contributing to improved forecast accuracy. These findings suggest that the synthesis of ML models and DBPS enables more reliable forecasting and improved uncertainty quantification.