Time-segmented scatter plots:A view on time-dependent state relations in discrete-event time series

Pairs of discrete event time series are characterised by their asynchronous nature, often hampering direct application of otherwise common analysis methods. For correct application of scatter plots, pairs of discrete event time series first have to be pre-processed and merged into a new synthetic time series of so-called co-observations. While standard scatter plots suggest analysis of global state correlation, connected scatter plots support more sophisticated hypotheses, by including sequence information. The family of time-segmented scatter plots introduced here additionally contributes time information, by dividing co-observations into time-related coloured segments. Time-segmented scatter plots permit to correlate co-observation states, state patterns and state relationships with time intervals, in order to explore time-stability of state relationships, discover otherwise overlooked dynamic patterns and possibly detect underlying processes that shape the formation of co-observation relationships. Enhanced concepts like filtered, tiled or delimited time-segmented scatter plots are available for unfavourable conditions like very high number of co-observations, overplotting, high variance or low autocorrelation. These extensions add visual aids to focus on the basic nature of co-observation relationships and their possible development. All concepts introduced in this paper are illustrated by means of a simple cash and carry warehouse example model.