Due to the special electromagnetic properties, high temperature superconducting (HTS) conductors become the potential solution for ultra-high field magnet and energy storage applications. However, screening current induced field (SCIF) have been demonstrated to be the main limitation to high field HTS magnets in actual applications. Based on time series models, this paper presents a prediction method of SCIF to support the design and application of HTS magnets. First, we analyze the data characteristic of SCIF hysteresis loop. The simulated dataset is prepared for two typical magnet structures: single pancake and solenoid. Then, time series models are proposed for the SCIF prediction. Through the intuitive analysis and the evaluation metrics, the training performance of time series models is confirmed. After discussion on hyper-parameters and dimension reduction, the optimized prediction performance is obtained for the SCIF hysteresis loop. In conjunction with the iterative prediction mode, it finally achieves the feasible and effective prediction method of SCIF for HTS magnets. It will provide a tool and research strategy to support the general finite element method.