Inference of financial networks using the normalised mutual information rate

Goh, Yong Kheng; Hasim, Haslifah Mohamad; Antonopoulos, Chris G.

doi:10.1371/journal.pone.0192160

Cited by 7 publications

(14 citation statements)

References 56 publications

(103 reference statements)

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“…-Distances using mutual information, mutual information rate, and other information-theoretic distances [28,26,29,30,31,32],…”

Section: On Distancesmentioning

confidence: 99%

A review of two decades of correlations, hierarchies, networks and clustering in financial markets

Marti,

Nielsen,

Bińkowski

et al. 2017

Preprint

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We review the state of the art of clustering financial time series and the study of their correlations alongside other interaction networks. The aim of the review is to gather in one place the relevant material from different fields, e.g. machine learning, econophysics, statistical physics, econometrics, behavioral finance. We hope it will help researchers to use more effectively this alternative modeling of the financial time series. Decision makers may also be able to leverage its insights. Finally, we also hope that this review will form the basis of an open toolbox to study correlations, hierarchies, networks and clustering in financial markets.

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“…-Distances using mutual information, mutual information rate, and other information-theoretic distances [28,26,29,30,31,32],…”

Section: On Distancesmentioning

confidence: 99%

A review of two decades of correlations, hierarchies, networks and clustering in financial markets

Marti,

Nielsen,

Bińkowski

et al. 2017

Preprint

View full text Add to dashboard Cite

show abstract

“…In this paper, we are using an information-theoretical methodology and statistical significance tests complemented by the false discovery rate (FDR) method for multiple hypothesis testing to infer connectivity in complex networks using only time-series data [37,38]. The data are recorded on the nodes of the network.…”

Section: Introductionmentioning

confidence: 99%

“…This allows to quantify how successful the network inference is. Our methodology is based on: (a) estimations of the Mutual Information Rate (MIR) for pairs of time-series (that represent pairs of nodes in the network) [37,38] and (b) on statistical significance tests to accept or reject connectivity using the false discovery rate method for multiple hypothesis testing.…”

Section: Introductionmentioning

confidence: 99%

“…MIR is the rate of information exchanged per unit of time between pairs of time-series [39,37,38] and is an appropriate measure to quantify the exchange of information in systems with correlation [40,33,39]. A normalised version of MIR has been shown to perform well in inferring the structure of networks in different cases of dynamics [37] and, in financial and stock markets data [38]. The authors in [37] discuss how to calculate MIR for Markov partitions.…”

Section: Introductionmentioning

confidence: 99%

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Network inference combining mutual information rate and statistical tests

Antonopoulos¹

2022

Preprint

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In this paper, we present a method that combines information-theoretical and statistical approaches to infer connectivity in complex networks using time-series data. The method is based on estimations of the Mutual Information Rate for pairs of time-series and on statistical significance tests for connectivity acceptance using the false discovery rate method for multiple hypothesis testing. We provide the mathematical background on Mutual Information Rate, discuss the statistical significance tests and the false discovery rate. Further on, we present results for correlated normal-variates data, coupled circle and coupled logistic maps, coupled Lorenz systems and coupled stochastic Kuramoto phase oscillators. Following up, we study the effect of noise on the presented methodology in networks of coupled stochastic Kuramoto phase oscillators and of coupling heterogeneity degree on networks of coupled circle maps. We show that the method can infer the correct number and pairs of connected nodes, by means of receiver operating characteristic curves. In the more realistic case of stochastic data, we demonstrate its ability to infer the structure of the initial connectivity matrices. The method is also shown to recover the initial connectivity matrices for dynamics on the nodes of Erdős-Rényi and small-world networks with varying coupling heterogeneity in their connections. The highlight of the proposed methodology is its ability to infer the underlying network connectivity based solely on the recorded datasets.

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“…Mutual information, the fundamental mathematical quantity of information theory, provides a universal way to quantify dependencies, transmission rates, and representations of data [1]. It has become an indispensable tool in many domains such as signal processing, data compression, finance, dynamical systems, and neuroscience [2][3][4][5][6][7]. Mutual information quantifies the information that one random variable carries about another by measuring the reduction in uncertainty about a given variable from knowing another variable.…”

Section: Introductionmentioning

confidence: 99%

Information estimation using nonparametric copulas

et al. 2018

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Estimation of mutual information between random variables has become crucial in a range of fields, from physics to neuroscience to finance. Estimating information accurately over a wide range of conditions relies on the development of flexible methods to describe statistical dependencies among variables, without imposing potentially invalid assumptions on the data. Such methods are needed in cases that lack prior knowledge of their statistical properties and that have limited sample numbers. Here we propose a powerful and generally applicable information estimator based on non-parametric copulas. This estimator, called the non-parametric copula-based estimator (NPC), is tailored to take into account detailed stochastic relationships in the data independently of the data’s marginal distributions. The NPC estimator can be used both for continuous and discrete numerical variables and thus provides a single framework for the mutual information estimation of both continuous and discrete data. By extensive validation on artificial samples drawn from various statistical distributions, we found that the NPC estimator compares well against commonly used alternatives. Unlike methods not based on copulas, it allows an estimation of information that is robust to changes of the details of the marginal distributions. Unlike parametric copula methods, it remains accurate regardless of the precise form of the interactions between the variables. In addition, the NPC estimator had accurate information estimates even at low sample numbers, in comparison to alternative estimators. The NPC estimator therefore provides a good balance between general applicability to arbitrarily shaped statistical dependencies in the data and shows accurate and robust performance when working with small sample sizes. We anticipate that the non-parametric copula information estimator will be a powerful tool in estimating mutual information between a broad range of data.

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Inference of financial networks using the normalised mutual information rate

Cited by 7 publications

References 56 publications

A review of two decades of correlations, hierarchies, networks and clustering in financial markets

A review of two decades of correlations, hierarchies, networks and clustering in financial markets

Network inference combining mutual information rate and statistical tests

Information estimation using nonparametric copulas

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