Calibration for Computer Models with Time-Varying Parameter

Traditional calibration methods often assume constant parameters that remain unchanged across input conditions, which can limit predictive accuracy when parameters actually vary. To address this issue, we propose a novel calibration framework with time-varying parameters. Building on the idea of profile least squares, we first apply local linear smoothing to estimate the discrepancy function between the computer model and the true process, and then use local linear smoothing again to obtain pointwise estimates of the functional calibration parameter. Through rigorous theoretical analysis, we establish the consistency and asymptotic normality of the proposed estimator. Simulation studies and an application to NASA’s OCO-2 mission demonstrate that the proposed method effectively captures parameter variation and improves predictive performance.