Quantum Bayesian Time Series Forecasting with Uncertainty Quantification
- 1University of Ilorin
Abstract
This study thoroughly evaluates a Quantum Bayesian Time Series Forecasting model, focusing on how well it can measure uncertainty in different types of noise and with varying numbers of data points. The paper compared the model‘s performance using several key metrics” Mean Squared Error (MSE), Mean Absolute Error (MAE), Coverage at 95%, Aleatoric and Epistemic uncertainty” against both synthetic noise models (heteroscedastic, heavy-tailed, homoscedastic, and regime-dependent) and real financial data. The results highlighted quantum advantages in breaking down uncertainty, especially in situations where data is volatile or not stable over time. Using a Bayesian time series model, the study obtained average levels of aleatoric and epistemic uncertainty for each assumption at different forecast sample sizes ”60-, 120-, 180-, and 240- time units (which can be years). The heavy-tailed error model performed best, with the lowest MSE and MAE across many sample sizes, such as MSE of 1.71 at sample size 60 and a high coverage of 0. The regime-dependent model performed well in one situation (lowest MSE of 1). The paper showed that including heavy-tailed errors and accounting for regime changes improved the accuracy and reliability of Bayesian forecasts. These results suggested that both aleatoric and epistemic uncertainty should be modelled in time series data, as done in full predictive density approaches, and have important implications for forecasting in financial, economic, or environmental contexts where volatility and sudden changes are common.Keywords: Bayesian; Quantum Computing, Simulation; Time Series; Forecasting
Related
- SGA: Uncertainty Quantification for Multi-Step Forecasting in Time Series Foundation Models
- Volatility-Corrected Prediction Intervals: Locally Adaptive Uncertainty Quantification for Probabilistic Time-Series Forecasting
- Online Bayesian Model Averaging with Joint Uncertainty Quantification for Models and Regression Coefficients in Binary Regression
- Enhanced Uncertainty Quantification Variational Autoencoders for the Solution of Bayesian Inverse Problems
- Uncertainty Quantification of State Variables Trajectories in the Context of Inverse Problems: An Approach from Bayesian Inference and FDA
BibTeX
@article{oloyede2026quantum,
title = {{Quantum Bayesian Time Series Forecasting with Uncertainty Quantification}},
author = {Isiaka Oloyede},
journal = {Reliability: Theory \& Applications},
year = {2026},
month = jun,
doi = {10.66721/3s6jbr20},
url = {https://doi.org/10.66721/3s6jbr20},
note = {CC BY-NC},
}
RIS
TY - JOUR
TI - Quantum Bayesian Time Series Forecasting with Uncertainty Quantification
AU - Isiaka Oloyede
PY - 2026
DA - 2026/06/01
JO - Reliability: Theory & Applications
DO - 10.66721/3s6jbr20
UR - https://doi.org/10.66721/3s6jbr20
AB - This study thoroughly evaluates a Quantum Bayesian Time Series Forecasting model, focusing on how well it can measure uncertainty in different types of noise and with varying numbers of data points. The paper compared the model‘s performance using several key metrics” Mean Squared Error (MSE), Mean Absolute Error (MAE), Coverage at 95%, Aleatoric and Epistemic uncertainty” against both synthetic noise models (heteroscedastic, heavy-tailed, homoscedastic, and regime-dependent) and real financial data. The results highlighted quantum advantages in breaking down uncertainty, especially in situations where data is volatile or not stable over time. Using a Bayesian time series model, the study obtained average levels of aleatoric and epistemic uncertainty for each assumption at different forecast sample sizes ”60-, 120-, 180-, and 240- time units (which can be years). The heavy-tailed error model performed best, with the lowest MSE and MAE across many sample sizes, such as MSE of 1.71 at sample size 60 and a high coverage of 0. The regime-dependent model performed well in one situation (lowest MSE of 1). The paper showed that including heavy-tailed errors and accounting for regime changes improved the accuracy and reliability of Bayesian forecasts. These results suggested that both aleatoric and epistemic uncertainty should be modelled in time series data, as done in full predictive density approaches, and have important implications for forecasting in financial, economic, or environmental contexts where volatility and sudden changes are common.Keywords: Bayesian; Quantum Computing, Simulation; Time Series; Forecasting
SN - 1932-2321
ER -