In this paper, we derive new satellite orbit and clock error models for time sequential, dual frequency, multi-constellation Advanced Receiver Autonomous Integrity Monitoring (ARAIM). In the current implementation of baseline 'snapshot' ARAIM, Carrier Smoothed Code (CSC) measurements at one instant in time are used to provide a navigation solution. Using a time-sequential implementation of ARAIM, i.e., using measurements collected over time, will significantly reduce Protection Levels (PL). It was shown in  that snapshot ARAIM cannot provide better performance than LPV-200, which has a 35 m Alert Limit (AL). Exploiting satellite motion will lead to superior positioning performance and significantly tighter PLs relative to baseline snapshot ARAIM, possibly even achieving 10 m ALs to support Category II aircraft approaches. In order to implement this time sequential approach, orbit and clock errors need to be characterized over time. In this paper, we process GPS and Galileo orbit and clock data to evaluate and analyze ranging errors over time. We then determine upper and lower bounds on ranging errors autocorrelation functions. These bounds will be implemented to over-bound time-sequential positioning errors.