A Tool to Measure Dependencies in Data Sequencesbernd

We present a general mathematical tool to measure statistical dependencies in data sequences. The method is based on a quantity called generalized mutual informationn (GMI). There are two essentials characterizing the proposed method: 1. The GMI considers all (linear and nonlinear) dependencies on a given quantization level; 2. There are eecient algorithms to estimate the GMI from nite data sequences. Our method can be applied, for instance, to an ergodic time series leading to the soocalled auto GMI functionn which can be considered as a nonlinear generalization of the welllknown autocorrelation function. Cross dependencies between two or more data sequences can be investigated as well. In any case, there must be at least 1000 data in the sequence, and it has to be almostt continuous in amplitude (say not less than 256 quantization steps). In this paper we deene the GMI and then summarize some of its properties and interpretations. Moreover, we sketch a fast estimation algorithm. For illustration we apply our method to some time series originating from diierent sources.