Dynamic complexity
A measure that captures the richness of a time course: amplitude, frequency and distribution in one.
Dynamic complexity is a measure for time series that combines the amplitude and frequency of fluctuations with the distribution of the measured values across the range of the scale. It is usually calculated within a moving window, so that the course of complexity itself over time becomes visible.
Whereas an average flattens a series into a single number, this measure tries to capture how rich and how changeable a time course is. A time series that moves calmly at one moment and violently the next, that shows both large and small deflections and makes use of the full range of the scale, receives a high dynamic complexity; a flat, monotonous series a low one. It is, one might say, a measure of the liveliness of a signal.
Measuring an approaching shift
Its clinical value lies above all in that moving window. Because the measure shows the course of complexity over time, it can reveal peaks associated with a critical instability, the unrest that precedes an order transition. In Schiepek's Synergetic Navigation System, dynamic complexity is therefore used to detect approaching turning points in the course of therapy on the basis of daily self-ratings.
A caveat belongs here: a measure is an aid, not an oracle. The value of dynamic complexity lies not in a number as such, but in what it helps to make visible, together with the conversation and the clinical eye: that a meaningful movement may be hidden beneath a seemingly erratic course, and that it is worth attending to it at the right moment.