Monte Carlo Dropout Neural Networks for Forecasting Sinusoidal Time Series: Performance Evaluation and Uncertainty Quantification

Abstract

Accurately forecasting sinusoidal time series is essential in various scientific and engineering applications. However, traditional models such as the seasonal autoregressive integrated moving average (SARIMA) rely on assumptions of linearity and stationarity, which may not adequately capture the complex periodic behaviors of sinusoidal data, including varying amplitudes, phase shifts, and nonlinear trends. This study investigates Monte Carlo dropout neural networks (MCDO NNs) as an alternative approach for both forecasting and uncertainty quantification. The performance of MCDO NNs is evaluated across six sinusoidal time series models, each exhibiting different dynamic characteristics. Results indicate that MCDO NNs consistently outperform SARIMA in terms of root mean square error, mean absolute percentage error, and the coefficient of determination, while also producing more reliable prediction intervals. To assess real-world applicability, the airline passenger dataset is used, demonstrating MCDO’s ability to effectively capture periodic structures. These findings suggest that MCDO NNs provide a robust alternative to SARIMA for sinusoidal time series forecasting, offering both improved accuracy and well-calibrated uncertainty estimates.