As power electronics continue to advance toward the MHz regime, existing magnetic hysteresis models exhibit reduced accuracy at high frequencies. While the Jiles–Atherton (JA) model remains widely used for its physical foundation and compactness, its Verilog-A and other implementations fail to capture the transient hysteresis at high frequencies. A physically motivated delay parameter tau_d is introduced into the Verilog-A model to compensate for the observed voltage-current phase deviation. The tau_d is estimated via Fourier analysis and incorporated into the flux density computation. Model parameters are identified using Bayesian optimization with an objective combining hysteresis loop features and core loss metrics. The modified model is validated on MnZn ferrites across various frequencies and flux densities. Results show excellent agreement between simulated and measured hysteresis loops and core losses, with relative core-loss errors below 4% up to 1 MHz. The proposed approach significantly extends the high-frequency applicability of JA-based models for accurate time-domain hysteresis and core-loss prediction.