Time Series Analysis - Trying to Solve an Inverse Problem

J. Timmer, Fakultät für Physik, Hermann-Herder-Str. 3, 79104 Freiburg, Germany

The behavior of many complex systems can be understood by models based on first principles. Often, however, only dynamical data of the complex system are available. Inference about the dynamics of the system based on measured time series is an inverse problem. This problem can usually only be solved by including additional knowledge about the system.

We exemplify this approach of investigating complex dynamical processes by an analysis of time series of human tremor. For the type of considered tremor it is of importance to decide on the respective contributions of reflexes, central oscillators and random effects to the tremor. We show that this question can be decided based on measured data.