Physical activity is disrupted in many psychiatric disorders. Advances in everyday technologies – such as accelerometers in smart phones – opens exciting possibilities for non-intrusive acquisition of activity data. Successful exploitation of this opportunity requires the validation of analytical methods that can capture the full movement spectrum. The study aim was to demonstrate an analytical approach to characterise accelerometer-derived activity patterns. Here, we use statistical methods to characterize accelerometer-derived activity patterns from a heterogeneous sample of 99 community-based adults with mental illnesses. Diagnoses were screened using the Mini International Neuropsychiatric Interview, and participants wore accelerometers for one week. We studied the relative ability of simple (exponential), complex (heavy-tailed), and composite models to explain patterns of activity and inactivity. Activity during wakefulness was a composite of brief random (exponential) movements and complex (heavy-tailed) processes, whereas movement during sleep lacked the heavy-tailed component. In contrast, inactivity followed a heavy-tailed process, lacking the random component. Activity patterns differed in nature between those with a diagnosis of bipolar disorder and a primary psychotic disorder. These results show the potential of complex models to quantify the rich nature of human movement captured by accelerometry during wake and sleep, and the interaction with diagnosis and health.