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• Kowalski, A
• Martin, M
• Plastino, A
• Judge, G
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• Martin, M
• Plastino, A
• Judge, G
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• Kowalski, A
• Martin, M
• Plastino, A
• Judge, G

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Entropy 2012, 14(10), 1829-1841; doi:10.3390/e14101829

Article

On Extracting Probability Distribution Information from Time Series

Andres M. Kowalski ^1,2 , Maria Teresa Martin ² , Angelo Plastino ^2,3,*  and George Judge ^4,†

¹ CIC Buenos Aires, C. C. 67, 1900 La Plata, Argentina ² Instituto de F ísica La Plata–CCT-CONICET, C.C. 727, 1900 La Plata, Argentina ³ IFISC (CSIC-UIB), Campues Universitat Illes Balears, E-07122 Palma de Mallorca, Spain ⁴ 207 Giannini Hall, University of California, Berkeley, Berkeley, CA 94720, USA ^† Member of the Giannini Foundation.

* Author to whom correspondence should be addressed.

Received: 15 August 2012; in revised form: 8 September 2012 / Accepted: 21 September 2012 / Published: 28 September 2012

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Abstract: Time-series (TS) are employed in a variety of academic disciplines. In this paper we focus on extracting probability density functions (PDFs) from TS to gain an insight into the underlying dynamic processes. On discussing this “extraction” problem, we consider two popular approaches that we identify as histograms and Bandt–Pompe. We use an information-theoretic method to objectively compare the information content of the concomitant PDFs.

Keywords: Bandt–Pompe; histograms; time-series

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