Irreversibility of financial time series: A graph-theoretical approach

Flanagan, Ryan; Lacasa, Lucas

doi:10.1016/j.physleta.2016.03.011

Cited by 98 publications

(64 citation statements)

References 46 publications

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“…A stochastic process is said to be time reversible if its probabilistic properties are invariant with respect to time reversal, other-wise it is directional or irreversible [1,2,3]. Recent reports describe the time irreversibility from different perspectives such as temporal asymmetry [4,5], complex network [6], visibility graph [7,8], entropy production [9,10], symbolic methods [11,12], and others. Based on the theoretical definitions [3], measures for time irreversibility generally target on the divergences in joint probability distributions between the forward and backward time series [9,13,14] or the probabilistic differences between symmetric distributions [5,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

Quantifying time irreversibility using probabilistic differences between symmetric permutations

Yao

Wang

et al. 2019

Physics Letters A

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To simplify the quantification of time irreversibility, we employ order patterns instead of the raw multidimension vectors in time series, and considering the existence of forbidden permutation, we propose a subtraction-based parameter, Y S , to measure the probabilistic differences between symmetric permutations for time irreversibility. Two chaotic models, the logistic and Henon systems, and reversible Gaussian process and their surrogate data are used to validate the time-irreversible measure, and time irreversibility of epileptic EEGs from Nanjing General Hospital is detected by the parameter. Test results prove that it is promising to quantify time irreversibility by measuring the subtraction-based probabilistic differences between symmetric order patterns, and our findings highlight the manifestation of nonlinearity of whether healthy or diseased EEGs and suggest that the epilepsy leads to a decline in the nonlinearity of brain electrical activities during seize-free intervals.

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Section: Introductionmentioning

confidence: 99%

Quantifying time irreversibility using probabilistic differences between symmetric permutations

Yao

Wang

et al. 2019

Physics Letters A

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“…Using the time series T = [3,5,9,11,14,1,7,10] as an example, the algorithm first divides the sequence into the odd and even parts iteratively. This steps enables the generation of a new ordered sequence T ′ = [3,14,9,7,5,1,11,10]. Finally, the butterfly operation is performed on T ′ , and this generates a new sequence, as shown in Figure 3…”

Section: Traditional Fft Algorithmmentioning

confidence: 99%

“…Using the sample time series T = [3,5,9,11,14,1,7,10], according to Figure 4, we get the original indices for each element in T as [0,1,2,3,4,5,6,7] and their binary codes. Specifically, for element 11 with index =3, the binary code (3) is '110.'…”

Section: Parallel Fft Algorithmmentioning

confidence: 99%

“…A time series is a sequence of data items or observations that are ordered in time. Time series data sets are produced in a variety of applications, including financial data analysis, medical and health monitoring, and industrial automation applications . In the financial domain, time series can keep track of stock prices, currency rates, or commodity prices over time.…”

Section: Introductionmentioning

confidence: 99%

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Parallel time series join using spark

Rong

Chen

Silva

2019

Concurrency and Computation

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Summary A time series is a sequence of data points in successive temporal order. Time series data is produced in many applications scenarios, and the techniques for its analysis have generated substantial interest. Time series join is a primitive operation that retrieves all pairs of correlated subsequences from two given time series. As the Pearson correlation coefficient, a measure of the correlation between two variables, has multiple beneficial mathematical properties, for example, the fact that it is invariant with respect to scale and offset, it is used to measure the correlation between two time series. Considering the need to analyze big time series data, we focus on the study of scalable and distributed techniques to process massive data sets. Specifically, we propose a parallel approach to perform time series joins using Spark, a popular analytics engine for large‐scale data processing. Our solution builds on (1) a fast method to compute the fast Fourier transform on the times series to calculate the correlation between two time series, (2) a lossless partition method to divide the time series into multiple subsequences and enable a parallel and correct computation of the join result, and (3) optimization techniques to avoid redundant computations. We performed extensive tests and showed that the proposed approach is efficient and scalable across different data sets and test configurations.

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“…Similarly, the graph-theoretical description of canonical routes to chaos [8][9][10][11] and some classical stochastic processes [6,12] have been discussed recently under this approach, as well as the exploration of relevant statistical properties such as time irreversibility [13,14]. From an applied perspective, these methods are routinely used to describe in combinatorial and topological terms experimental signals emerging in different fields including physics [15][16][17][18][19][20][21], neuroscience [22][23][24][25] or finance [26] to cite a few examples where analysis and classification of such signals is relevant.…”

Section: Introductionmentioning

confidence: 99%

Visibility graphs and symbolic dynamics

Lacasa

Just

2018

Physica D: Nonlinear Phenomena

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Visibility algorithms are a family of geometric and ordering criteria by which a real-valued time series of N data is mapped into a graph of N nodes. This graph has been shown to often inherit in its topology nontrivial properties of the series structure, and can thus be seen as a combinatorial representation of a dynamical system. Here we explore in some detail the relation between visibility graphs and symbolic dynamics. To do that, we consider the degree sequence of horizontal visibility graphs generated by the one-parameter logistic map, for a range of values of the parameter for which the map shows chaotic behaviour. Numerically, we observe that in the chaotic region the block entropies of these sequences systematically converge to the Lyapunov exponent of the system. Via Pesin identity, this in turn suggests that these block entropies are converging to the Kolmogorov-Sinai entropy of the map, which ultimately suggests that the algorithm is implicitly and adaptively constructing phase space partitions which might have the generating property. To give analytical insight, we explore the relation k(x), x ∈ [0, 1] that, for a given datum with value x, assigns in graph space a node with degree k. In the case of the out-degree sequence, such relation is indeed a piece-wise constant function. By making use of explicit methods and tools from symbolic dynamics we are able to analytically show that the algorithm indeed performs an effective partition of the phase space and that such partition is naturally expressed as a countable union of subintervals, where the endpoints of each subinterval are related to the fixed point structure of the iterates of the map and the subinterval enumeration is associated with particular ordering structures that we called motifs.

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Irreversibility of financial time series: A graph-theoretical approach

Cited by 98 publications

References 46 publications

Quantifying time irreversibility using probabilistic differences between symmetric permutations

Quantifying time irreversibility using probabilistic differences between symmetric permutations

Parallel time series join using spark

Visibility graphs and symbolic dynamics

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