FLUCTUATION SPECTROSCOPY

We review the thermodynamics of estimating the statistical fluctuation s of an observed process. Since any statistical analysis involves a ch oice of model class-either explicitly or implicitly -we demonstrate th e benefits of a careful choice. For each of three classes a particular model is reconstructed from data streams generated by four sample pro cesses. Then each estimated model's thermodynamic structure is used to estimate the typical behavior and the magnitude of deviations for the observed system. These arc then compared to the known fluctuation pro perties. The type of analysis advocated here, which uses estimated mod el class information, recovers the correct statistical structure of th ese processes from simulated data. The current alternative-direct esti mation of the Renyi entropy from time series histograms-uses neither p rior nor reconstructed knowledge of the model class. And, in most case s, it fails to recover the process's statistical structure from finite data-unpredictability is overestimated. In this analysis, we introduc e the fluctuation complexity as a measure of a process's total range o f allowed statistical variation. It is a new and complementary charact eristic in that it differs from the process's information production r ate and its memory capacity.