  Car-following behavior modeling is critical for understanding traffic flow
dynamics and developing high-fidelity microscopic simulation models. Most
existing impulse-response car-following models prioritize computational
efficiency and interpretability by using a parsimonious nonlinear function
based on immediate preceding state observations. However, this approach
disregards historical information, limiting its ability to explain real-world
driving data. Consequently, serially correlated residuals are commonly observed
when calibrating these models with actual trajectory data, hindering their
ability to capture complex and stochastic phenomena. To address this
limitation, we propose a dynamic regression framework incorporating time series
models, such as autoregressive processes, to capture error dynamics. This
statistically rigorous calibration outperforms the simple assumption of
independent errors and enables more accurate simulation and prediction by
leveraging higher-order historical information. We validate the effectiveness
of our framework using HighD and OpenACC data, demonstrating improved
probabilistic simulations. In summary, our framework preserves the parsimonious
nature of traditional car-following models while offering enhanced
probabilistic simulations. The code of this work is available at
https://github.com/Chengyuan-Zhang/IDM_Bayesian_Calibration.
