MODELING OF CIRCADIAN RHYTHMS USING HYBRID TIME SERIES MODEL, POLYNOMIAL REGRESSION, NNAR, AND BAYESIAN-ARIMA TIME SERIES FORECASTING METHODS

Circadian rhythms, characterized by their high periodicity, are ideally suited for time series statistical modeling. This study comparatively analyzes four approaches: TBATS (a hybrid time series model), polynomial regression, neural network autoregression, and a Bayesian formulation of the (autoregressive integrated moving average) ARIMA model for modeling and forecasting 24-hour core body temperature fluctuations. Hourly temperature data were evaluated using root mean square error (RMSE) as the primary accuracy criterion. The hybrid model (TBATS), which incorporates Box-Cox transformation, trend smoothing, trigonometric seasonal decomposition, and (autoregressive moving average) ARMA errors, captured long-term rhythmicity and short-term autocorrelation with high fidelity. A fourth-order polynomial regression provided a flexible exploratory fit but showed signs of overfitting, especially near temporal extremes. The Bayesian ARIMA model accounted for the autocorrelation structure while providing credible intervals for parameter uncertainty, but struggled to effectively capture circadian periodicity. NNAR and TBATS outperformed both alternatives in terms of predictive performance and fit to the biological characteristics of the data. Incorporating Bayesian inference improved the model’s interpretability and enabled the integration of prior knowledge, making it particularly valuable in clinical and experimental settings. These results highlight the need to adapt the model structure to the characteristics of biological time series and support the use of hybrid and probabilistic models in circadian rhythm research. Future studies should explore the model’s generalizability across multi-day cycles, evaluate performance in populations with circadian disruptions, and consider the inclusion of covariates such as light exposure or sleep-wake cycles to improve biological interpretability and prediction accuracy.