Extracellular recordings in the area of the subthalamic nucleus (STN) of Parkinson's disease patients undergoing deep brain stimulation comprise fast events, Action Potentials and slower events, known as Local Field Potentials (LFP). The LFP is believed to represent the synchronized input into the observed area, as opposed to the spike data, which represents the output. We have shown before that there is an input-output relationship between these two components in the STN. In the present paper, we extend these observations by using LFP-driven Volterra models and the Laguerre expansion technique to estimate nonlinear dynamic models which are able to predict the recorded spiking activity. To this end, we rigorously examine the optimal model order. The improved performance of the second-order Volterra models indicates that there is a nonlinear relationship between the LFP and the spiking activity. To obtain a more compact and readily interpretable model, the most significant dynamic components of the identified Volterra models are extracted using principal dynamic mode analysis.