We describe how to analyze the wide class of non-stationary processes with stationary centered increments using Shannon information theory. To do so, we use a practical viewpoint and define ersatz quantities from time-averaged probability distributions. These ersatz versions of entropy, mutual information, and entropy rate can be estimated when only a single realization of the process is available. We abundantly illustrate our approach by analyzing Gaussian and non-Gaussian self-similar signals, as well as multi-fractal signals. Using Gaussian signals allows us to check that our approach is robust in the sense that all quantities behave as expected from analytical derivations. Using the stationarity (independence on the integration time) of the ersatz entropy rate, we show that this quantity is not only able to fine probe the self-similarity of the process, but also offers a new way to quantify the multi-fractality.
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Univ N Carolina, Dept Math & Stat, Greensboro, NC 27412 USAUniv N Carolina, Dept Math & Stat, Greensboro, NC 27412 USA
Zhang, Haimeng
Huang, Chunfeng
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Indiana Univ, Dept Stat, Bloomington, IN 47408 USA
Indiana Univ, Dept Geog, Bloomington, IN 47408 USAUniv N Carolina, Dept Math & Stat, Greensboro, NC 27412 USA
机构:
Columbia Univ, Grad Sch Business, Business, New York, NY 10027 USAColumbia Univ, Grad Sch Business, Business, New York, NY 10027 USA
Besbes, Omar
Gur, Yonatan
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Stanford Univ, Grad Sch Business, Operat Informat & Technol, Stanford, CA 94305 USAColumbia Univ, Grad Sch Business, Business, New York, NY 10027 USA
Gur, Yonatan
Zeevi, Assaf
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Columbia Univ, Grad Sch Business, Business, New York, NY 10027 USAColumbia Univ, Grad Sch Business, Business, New York, NY 10027 USA