Order Patterns in Time Series

Bandt, Christoph; Shiha, F. A.

doi:10.1111/j.1467-9892.2007.00528.x

Cited by 155 publications

(171 citation statements)

References 17 publications

(15 reference statements)

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“…The statistical properties of the empirical estimator and computations of expected values for some continuous distributions including Gaussian families are discussed in [21,22].…”

Section: Notation and Terminologymentioning

confidence: 99%

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Random Walk Null Models for Time Series Data

DeFord

Moore

2017

Entropy

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Permutation entropy has become a standard tool for time series analysis that exploits the temporal and ordinal relationships within data. Motivated by a Kullback-Leibler divergence interpretation of permutation entropy as divergence from white noise, we extend pattern-based methods to the setting of random walk data. We analyze random walk null models for correlated time series and describe a method for determining the corresponding ordinal pattern distributions. These null models more accurately reflect the observed pattern distributions in some economic data. This leads us to define a measure of complexity using the deviation of a time series from an associated random walk null model. We demonstrate the applicability of our methods using empirical data drawn from a variety of fields, including to a variety of stock market closing prices.

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“…The statistical properties of the empirical estimator and computations of expected values for some continuous distributions including Gaussian families are discussed in [21,22].…”

Section: Notation and Terminologymentioning

confidence: 99%

“…It is well known [21,24] that if the {Z i } n i=1 are exchangeable random variables, including the case of independent and identically distributed continuous random variables, then P Z (π) = 1 n! for all π ∈ S n .…”

Section: Permutation Entropy and Kl Divergencementioning

confidence: 99%

Random Walk Null Models for Time Series Data

DeFord

Moore

2017

Entropy

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“…1, is about 10 5 , depending on the pump power. The probabilities of patterns 012 and 210 provide a measure of the persistence of the time-series, i.e., the probability that the sign of x i − x i−1 persists in the next step [11]. Thus, at the transition, if there are two consecutive peaks with increasing height, the next peak is likely to be larger than the previous one (and if there are two consecutive peaks with decreasing height, the next one is likely to be smaller than the previous one); on the contrary, in the sequence of time-intervals, two consecutive intervals that are increasingly long (∆T i < ∆T i+1 ) are likely to be followed by shorter interval (∆T i+1 > ∆T i+2 ), and two consecutive decreasing intervals (∆T i > ∆T i+1 ) are likely to be followed by a longer one (∆T i+1 < ∆T i+2 ).…”

Section: The Two Analysis Methodsmentioning

confidence: 99%

Investigating optical complexity of the phase transition in the intensity of a fibre laser radiation

et al. 2016

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Fibre lasers have been shown to manifest a laminar-to-turbulent transition when increasing its pump power. In order to study the dynamical complexity of this transition we use advanced statistical tools of time-series analysis. We apply ordinal analysis and the horizontal visibility graph to the experimentally measured laser output intensity. This reveal the presence of temporal correlations during the transition from the laminar to the turbulent lasing regimes. Both methods allow us to unveil coherent structures with well defined time-scales and strong correlations both, in the timing of the laser pulses and in their peak intensities.

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“…The probability is estimated using the ordinal partitions symbolization [18,19]. The procedure transforms an experimental sample into a sequence of n-tuples called order patterns π of size n. Each π contains n indexes of the original sample.…”

Section: Conflicts Of Interestmentioning

confidence: 99%

Minimum Sample Size for Reliable Causal Inference Using Transfer Entropy

Ramos

Macau

2017

Entropy

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Transfer Entropy has been applied to experimental datasets to unveil causality between variables. In particular, its application to non-stationary systems has posed a great challenge due to restrictions on the sample size. Here, we have investigated the minimum sample size that produces a reliable causal inference. The methodology has been applied to two prototypical models: the linear model autoregressive-moving average and the non-linear logistic map. The relationship between the Transfer Entropy value and the sample size has been systematically examined. Additionally, we have shown the dependence of the reliable sample size and the strength of coupling between the variables. Our methodology offers a realistic lower bound for the sample size to produce a reliable outcome.

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Order Patterns in Time Series

Cited by 155 publications

References 17 publications

Random Walk Null Models for Time Series Data

Random Walk Null Models for Time Series Data

Investigating optical complexity of the phase transition in the intensity of a fibre laser radiation

Minimum Sample Size for Reliable Causal Inference Using Transfer Entropy

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