This work focuses on methods for investigation of physiological time series based on complexity analysis. It is a part of a wider programme to determine non-invasive markers for healthy ageing. We consider two case studies investigated with actigraphy: (a) sleep and alternations with insomnia, and (b) ageing effects on mobility patterns. We illustrate, using these case studies, the application of fractal analysis to the investigation of regulation patterns and control, and change of physiological function. In the first case study, fractal analysis techniques were implemented to study the correlations present in sleep actigraphy for individuals suffering from acute insomnia in comparison with healthy controls. The aim was to investigate if complexity analysis can detect the onset of adverse health-related events. The subjects with acute insomnia displayed significantly higher levels of complexity, possibly a result of too much activity in the underlying regulatory systems. The second case study considered mobility patterns during night time and their variations with age. It showed that complexity metrics can identify change in physiological function with ageing. Both studies demonstrated that complexity analysis can be used to investigate markers of health, disease and healthy ageing.