Insects can efficiently perform object motion detection via a specialized neural circuit, called an elementary motion detector (EMD). In contrast, conventional machine vision systems require significant computational resources for dynamic motion processing. Here, a fully memristive EMD (M-EMD) is presented that implements the Hassenstein-Reichardt (HR) correlator, a biological model of the EMD. The M-EMD consists of a simple Wye (Y) configuration, including a static resistor, a dynamic memristor, and a Mott memristor. The resistor and dynamic memristor introduce different signal delays, enabling spatio-temporal signal integration in the subsequent Mott memristor, resulting in a direction-selective response. In addition, a neuromorphic system is developed employing the M-EMDs to predict a lane-changing maneuver by vehicles on the road. The system achieved a high accuracy (> 87%) in predicting future lane-changing maneuvers on the Next Generation Simulation (NGSIM) dataset while reducing the computational cost by 92.9% compared to the conventional neuromorphic system without the M-EMD, suggesting its strong potential for edge-level computing.