This study extends Jump Models for dynamical systems by sampling observations from a distribution to estimate hidden states. It links the detection of financial time series price jumps with anomaly detection in time series segments. A new three-step method is proposed: 1) jump detection using Mahalanobis distance with path signatures; 2) training Jump Models with this indicator; and 3) predicting hidden states from new data. The approach enhances accuracy by identifying outliers post-jump; with analysis on simulated data showing the method's effectiveness in accurately retrieving true hidden states without relying on future information.