This paper proposes a method for determining the resolution for the processing of irregularly-sampled time series data to provide a balanced perspective of agents’ behaviour. The behaviour is described as a collection of prolonged events, which are characterised by start/open and end/close times in addition to other useful attributes. We propose the definition of an equilibrium resolution and carry out its analysis based on probabilistic assumptions. The resulting methods of determining the equilibrium resolution are tested on real-life time series data sets from the Financial and Travel problem domains.