Bandt-Pompe symbolization dynamics for time series with tied values: A data-driven approach

Traversaro, Francisco; Redelico, Francisco O.; Risk, Marcelo; Frery, Alejandro C.; Rosso, Osvaldo A.

doi:10.1063/1.5022021

Cited by 18 publications

(16 citation statements)

References 63 publications

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“…Originally, for time series with continuous values, Brandt and Pompe suggested adding a small random perturbation in this case, but while we worked with a symbolic description, this did not apply. In our research, we assumed that if x i = x j , then x i < x j if i < j; however, also other methods have been proposed [40,41]. In the case of PE, introducing symbolic description aims at providing a more precise description of the time series.…”

Section: Financial Data and Symbolic Representationmentioning

confidence: 99%

Permutation Entropy as a Measure of Information Gain/Loss in the Different Symbolic Descriptions of Financial Data

Kozák

Kania

Juszczuk

2020

Entropy

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Financial markets give a large number of trading opportunities. However, over-complicated systems make it very difficult to be effectively used by decision-makers. Volatility and noise present in the markets evoke a need to simplify the market picture derived for the decision-makers. Symbolic representation fits in this concept and greatly reduces data complexity. However, at the same time, some information from the market is lost. Our motivation is to answer the question: What is the impact of introducing different data representation on the overall amount of information derived for the decision-maker? We concentrate on the possibility of using entropy as a measure of the information gain/loss for the financial data, and as a basic form, we assume permutation entropy with later modifications. We investigate different symbolic representations and compare them with classical data representation in terms of entropy. The real-world data covering the time span of 10 years are used in the experiments. The results and the statistical verification show that extending the symbolic description of the time series does not affect the permutation entropy values.

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Section: Financial Data and Symbolic Representationmentioning

confidence: 99%

Permutation Entropy as a Measure of Information Gain/Loss in the Different Symbolic Descriptions of Financial Data

Kozák

Kania

Juszczuk

2020

Entropy

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“…For d = 1 the points are consecutive. Assume there are no ties between the neighboring points, which for continuous processes, or empirical data with decent resolution, should not be an issue (see also [19,20]). Three points can be arranged in six ways, identified by an order pattern π p (Fig.…”

Section: A Theorymentioning

confidence: 99%

Analytical representation of Gaussian processes in the A−T plane

Tarnopolski

2019

Phys. Rev. E

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Closed-form expressions, parametrized by the Hurst exponent H and the length n of a time series, are derived for paths of fractional Brownian motion (fBm) and fractional Gaussian noise (fGn) in the A − T plane, composed of the fraction of turning points T and the Abbe value A. The exact formula for A fBm is expressed via Riemann ζ and Hurwitz ζ functions. A very accurate approximation, yielding a simple exponential form, is obtained. Finite-size effects, introduced by the deviation of fGn's variance from unity, and asymptotic cases are discussed. Expressions for T for fBm, fGn, and differentiated fGn are also presented. The same methodology, valid for any Gaussian process, is applied to autoregressive moving average processes, for which regions of availability of the A − T plane are derived and given in analytic form. Locations in the A − T plane of some real-world examples as well as generated data are discussed for illustration. arXiv:1910.14018v3 [physics.data-an] 30 Dec 2019 123 321 132 231 213 312

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“…An interesting approach to get rid of tied values through imputation, although in the context of ordinal pattern statistics, is provided elsewhere in this volume. 16…”

Section: Tied Valuesmentioning

confidence: 99%

Nonlinear dynamics of river runoff elucidated by horizontal visibility graphs

Lange

Sippel

Rosso

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Horizontal Visibility Graphs (HVGs) are a recently developed method to construct networks from time series. The values of the time series are considered as the nodes of the network and are linked to each other if there is no larger value between them, such as they can "see" each other. The network properties reflect the nonlinear dynamics of the time series. For some classes of stochastic processes and for periodic time series, analytical results can be obtained for network-derived quantities such as the degree distribution, the local clustering coefficient distribution, the mean path length, and others. HVGs have the potential to discern between deterministic-chaotic and correlated-stochastic time series. Here, we investigate the sensitivity of the HVG methodology to properties and pre-processing of real-world data, i.e., time series length, the presence of ties, and deseasonalization, using a set of around 150 runoff time series from managed rivers at daily resolution from Brazil with an average length of 65 years. We show that an application of HVGs on real-world time series requires a careful consideration of data pre-processing steps and analysis methodology before robust results and interpretations can be obtained. For example, one recent analysis of the degree distribution of runoff records reported pronounced sub-exponential "long-tailed" behavior of North American rivers, whereas another study of South American rivers showed hyper-exponential "short-tailed" behavior resembling correlated noise. We demonstrate, using the dataset of Brazilian rivers, that these apparently contradictory results can be reconciled by minor differences in data-preprocessing (here: small differences in subtracting the seasonal cycle). Hence, data-preprocessing that is conventional in hydrology ("deseasonalization") changes long-term correlations and the overall runoff dynamics substantially, and we present empirical consequences and extensive simulations to investigate these issues from a HVG methodological perspective. After carefully accounting for these methodological aspects, the HVG analysis reveals that the river runoff dataset shows indeed complex behavior that appears to stem from a superposition of short-term correlated noise and "long-tailed behaviour," i.e., highly connected nodes. Moreover, the construction of a dam along a river tends to increase short-term correlations in runoff series. In summary, the present study illustrates the (often substantial) effects of methodological and data-preprocessing choices for the interpretation of river runoff dynamics in the HVG framework and its general applicability for real-world time series.

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Bandt-Pompe symbolization dynamics for time series with tied values: A data-driven approach

Cited by 18 publications

References 63 publications

Permutation Entropy as a Measure of Information Gain/Loss in the Different Symbolic Descriptions of Financial Data

Permutation Entropy as a Measure of Information Gain/Loss in the Different Symbolic Descriptions of Financial Data

Analytical representation of Gaussian processes in the A−T plane

Nonlinear dynamics of river runoff elucidated by horizontal visibility graphs

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