In the last half decade, nearly 31% of annual global deaths are linked to cardiovascular diseases. Thus, robotic catheterizations are recently proposed for interventions of conditions such as aneurism or atherosclerosis formed along vascular paths leading to the heart. However, existence of mild to strong hysteresis while navigating unactuated catheters with the current robotic systems inhibits autonomous control for vascular surgery. Thus, immersion of surgeons remains high with most of their time spent on steering the catheter in-and-out of the vessels. In this study, an autoregressive nonlinear neural network model is adapted for parameterization of vital causal factors of hysteresis during robotic catheterization. Crucial for autonomous control, hysteretic behaviors of endovascular tool are modeled while suitable values are estimated and analyzed for five contributory factors. The network model is validated with hysteresis data we obtained from a two degree-of-freedom robotic system and an unactuated catheter. Result validation shows accurate description of the hysteresis profile recorded duirng catheterization trials with a vascular phantom model.