Effects of dynamical time scale mismatch on time series analysis using event intervals

Abstract

The use of a sequence of inter-event time intervals as a proxy for time series measurements in state space reconstructions, used to compute correlation dimensions, is explored. In addition to testing the validity of the method in general, the effects of using time intervals that are much longer than the characteristic time scale of the system dynamics are examined. Two model systems for which copious information is available are employed: empirically measured data produced using a Chua circuit, and computed numerical values produced using a nonlinear model of the reproductive endocrine system. For time intervals well-matched to the dynamical time scale, the result of state space reconstructions using these time intervals is successful for both the Chua circuit data and the endocrine modeling results. Using longer time intervals, however, results in computed correlation dimensions that are considerably higher than the actual correlation dimensions of these systems. Similar results are also found using very long delay times in a standard time series analysis of the variables in both systems. Using parameter variations to induce changes in the correlation dimension of the endocrine model system, it is shown that these changes are similar in both the actual correlation dimension and the higher correlation dimension computed using very long time intervals. It is argued that this has important implications for studies in which the only available data consists of event intervals, as illustrated by comparisons between the endocrine modeling results presented here and empirical studies using menstrual cycle lengths as events intervals.