Objective. Since the discovery of the population vector that directly relates neural spiking activity with arm movement direction, it has become feasible to control robotic arms and neuroprostheses using invasively recorded brain signals. For non-invasive approaches, a direct relation between human brain signals and arm movement direction is yet to be established. Approach. Here, we investigated electroencephalographic (EEG) signals in temporal and spectral domains in a continuous, circular arm movement task. Using machine learning methods that respect the linear mixture of brain activity within EEG signals, we show that directional information is represented in the temporal domain in amplitude modulations of the same frequency as the arm movement, and in the spectral domain in power modulations of the 20–24 Hz frequency band. Main results. In the temporal domain, the directional information was mainly expressed in primary sensorimotor cortex (SM1) and posterior parietal cortex (PPC) contralateral to the moving arm, while in the spectral domain SM1 and PPC of both hemispheres predicted arm movement direction. The different cortical representations suggest distinct neural representations in both domains. Significance. This direct relation between neural activity and arm movement direction in both domains demonstrates the potential of machine learning to reveal neuroscientific insights about the dynamics of human arm movements.