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Autocorrelation type functions for big and dirty data series

One form of big data are signals - time series of consecutive values. In physical experiments, billions of values can now be measured within a second. Signals of heart and brain in intensive care, as well as seismic waves, are measured with 100 up to 1000 Hz over hours, days or even years. A song of 3 minutes on CD comprises 16 million values. Music and seismic vibrations basically consist of harmonic oscillations for which classical tools like autocorrelation and spectrogram work well. This note presents similar tools for all kinds of rhythmic processes, with non-linear distortion, artefacts, and outliers. Permutation entropy has been used in physics, medicine, and engineering. Big data allow a detailed analysis of ordinal patterns. As new version of permutation entropy, we define a distance to white noise consisting of four curious components. Applications to a variety of data are discussed.