Order patterns, their variation and change points in financial time series and Brownian motion

Bandt, Christoph

doi:10.1007/s00362-020-01171-7

Cited by 24 publications

(30 citation statements)

References 34 publications

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“…Consequently, the ordinal pattern probability distribution per se or, alternatively, the relative frequencies of some appropriately combined ordinal patterns can result which are, for particular purposes, even more useful than PE or WPE. This hypothesis has been supported by recent studies of Bandt [27,28], Cuesta-Frau et al [29] and Gunther et al [30]. Actually, it has been previously shown that hierarchies and probabilities of the ordinal patterns offer a better characterization of the dynamical regimes of some complex systems, identifying transitions and behaviors that are not detected by more traditional statistical tools [31][32][33][34].…”

Section: An Ordinal-patterns-based New Approach To Time-delay Identificationmentioning

confidence: 73%

Time-Delay Identification Using Multiscale Ordinal Quantifiers

Soriano

Zunino

2021

Entropy

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Time-delayed interactions naturally appear in a multitude of real-world systems due to the finite propagation speed of physical quantities. Often, the time scales of the interactions are unknown to an external observer and need to be inferred from time series of observed data. We explore, in this work, the properties of several ordinal-based quantifiers for the identification of time-delays from time series. To that end, we generate artificial time series of stochastic and deterministic time-delay models. We find that the presence of a nonlinearity in the generating model has consequences for the distribution of ordinal patterns and, consequently, on the delay-identification qualities of the quantifiers. Here, we put forward a novel ordinal-based quantifier that is particularly sensitive to nonlinearities in the generating model and compare it with previously-defined quantifiers. We conclude from our analysis on artificially generated data that the proper identification of the presence of a time-delay and its precise value from time series benefits from the complementary use of ordinal-based quantifiers and the standard autocorrelation function. We further validate these tools with a practical example on real-world data originating from the North Atlantic Oscillation weather phenomenon.

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Section: An Ordinal-patterns-based New Approach To Time-delay Identificationmentioning

confidence: 73%

Time-Delay Identification Using Multiscale Ordinal Quantifiers

Soriano

Zunino

2021

Entropy

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“…Therefore, the pairs of OrPs (2,2,1,5,3) and (2,2,5,1,3) in Fig. 2, which could instead be (4,4,1,5,3) and (4,4,5,1,3), are not symmetric. The 'NonE' AmPs of the symmetric vectors, i.e., (3,1,5,2,4) and (4,1,5,2,3), are also not symmetric.…”

Section: Equal Values In Ordinal Patternsmentioning

confidence: 99%

“…The coarse-grained ordinal method maps the time series into a sequence of permutations on the basis of a comparison of neighboring values. Ordinal approaches inherit the causal information about dynamical processes and have been widely used in fields such as physics, mathematics, engineering, and biomedicine [3].…”

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confidence: 99%

“…However, this approach is incorrect because the original symmetric permutations are not always equivalent to the permutations of symmetric vectors. To address this problem, researchers adopted an alternative ordinal scheme that faithfully reflects the temporal structure of vectors [3,6,7]. In this paper, we refer to that scheme as the amplitude permutation (AmP).…”

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confidence: 99%

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Comparative analysis of the original and amplitude permutations

Yao,

Wang

2021

Preprint

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We compare the two basic ordinal patterns, i.e., the original and amplitude permutations, used to characterize vector structures. The original permutation consists of the indexes of reorganized values in the original vector. By contrast, the amplitude permutation comprises the positions of values in the reordered vector, and it directly reflects the temporal structure. To accurately convey the structural characteristics of vectors, we modify indexes of equal values in permutations to be the same as, for example, the smallest or largest indexes in each group of equalities. Overall, we clarify the relationship between the original and amplitude permutations. And the results have implications for time-and amplitude-symmetric vectors and will lead to further theoretical and experimental studies.

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“…The study of change-points dates back to the 1950s when Page (1954Page ( , 1955 proposed some procedures to test the existence of a change in mean, and also to identify homogeneous subsets in a set of random samples. Since then various non-parametric and parametric methods have been developed; hence the corresponding literature is quite extensive, and such problems have been further raised in different contexts such as agronomy (Brault et al 2018), hydrology (Serinaldi et al 2018), environmental applications (Moura e Silva et al 2020), and finance (Bandt 2020). The methods are generally grouped in two main categories: online techniques which study the data as they become available and detect changes as soon as they happen in real time, and offline methods that assume all samples are already received.…”

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confidence: 99%

Locally adaptive change-point detection (LACPD) with applications to environmental changes

Moradi

Montesino

Ugarte

et al. 2021

Stoch Environ Res Risk Assess

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We propose an adaptive-sliding-window approach (LACPD) for the problem of change-point detection in a set of time-ordered observations. The proposed method is combined with sub-sampling techniques to compensate for the lack of enough data near the time series’ tails. Through a simulation study, we analyse its behaviour in the presence of an early/middle/late change-point in the mean, and compare its performance with some of the frequently used and recently developed change-point detection methods in terms of power, type I error probability, area under the ROC curves (AUC), absolute bias, variance, and root-mean-square error (RMSE). We conclude that LACPD outperforms other methods by maintaining a low type I error probability. Unlike some other methods, the performance of LACPD does not depend on the time index of change-points, and it generally has lower bias than other alternative methods. Moreover, in terms of variance and RMSE, it outperforms other methods when change-points are close to the time series’ tails, whereas it shows a similar (sometimes slightly poorer) performance as other methods when change-points are close to the middle of time series. Finally, we apply our proposal to two sets of real data: the well-known example of annual flow of the Nile river in Awsan, Egypt, from 1871 to 1970, and a novel remote sensing data application consisting of a 34-year time-series of satellite images of the Normalised Difference Vegetation Index in Wadi As-Sirham valley, Saudi Arabia, from 1986 to 2019. We conclude that LACPD shows a good performance in detecting the presence of a change as well as the time and magnitude of change in real conditions.

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Order patterns, their variation and change points in financial time series and Brownian motion

Cited by 24 publications

References 34 publications

Time-Delay Identification Using Multiscale Ordinal Quantifiers

Time-Delay Identification Using Multiscale Ordinal Quantifiers

Comparative analysis of the original and amplitude permutations

Locally adaptive change-point detection (LACPD) with applications to environmental changes

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