Standard Bayesian autoregressive changepoint models can become unstable near sample boundaries. As a candidate changepoint approaches either edge of the series, the local residual degrees of freedom shrink, producing a Gamma-function singularity in the marginal likelihood that can strongly bias the posterior toward spurious edge detections. To address this issue, we introduce a regularization framework driven by local degrees of freedom. By incorporating a centripetal prior of the form $\pi \left(k\right)\propto {\left({\nu }_1{\nu }_2\right)}^{\lambda }$—where ${\nu }_1=k-2p-1$ and ${\nu }_2=n-k-p-1$—the proposed method is designed to counteract this boundary effect. Theoretical analysis shows that a regularization intensity of $\lambda \ge 1$ is sufficient to offset this boundary effect asymptotically. Simulation results confirm that this approach substantially mitigates the U-shaped error profile typical of unregularized estimators, yielding a more favorable accuracy–robustness trade-off relative to the standard frequentist baselines considered in our study. Finally, empirical applications to several 2022 natural gas benchmarks, including TTF, SHPGX LNG, JKM, NBP, and NYMEX Henry Hub, demonstrate the framework’s ability to distinguish persistent structural transitions from transient market turbulence. These results suggest that degree-of-freedom-based centripetal prior regularization can improve the stability of Bayesian changepoint inference in nonstationary time series.