An Updated Literature Review of Distance Correlation and Its Applications to Time Series

Edelmann, Dominic; Fokianos, Konstantinos; Pitsillou, Maria

doi:10.1111/insr.12294

Cited by 41 publications

(25 citation statements)

References 93 publications

(242 reference statements)

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“…However, the Pearson correlation has its limitation. In some situations, the two variables with zero coefficient value may not be independent of each other as the Pearson correlation only detects the linear relationship between two variables, but not the non-linear relationship [47]. Hence, Székely et al [22] introduced a new correlation measure known as distance correlation, where it is zero if and only if the variables are independent.…”

Section: Determining the Interdependence Degrees Using Distance Corrementioning

confidence: 99%

An Alternate Unsupervised Technique Based on Distance Correlation and Shannon Entropy to Estimate λ0-Fuzzy Measure

2020

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λ0-measure is a special type of fuzzy measure. In the context of multi-attribute decision making (MADM), the measure can be used together with Choquet integral to model the interdependencies that usually present between the decision attributes. Unfortunately, the range of techniques available to estimate λ0-measure values is too limited i.e., only four techniques are available to this date. Besides, the review on literature shows that each of these existing techniques either requires some initial data from the decision-makers or misrepresents the actual interdependencies held by the attributes. Thus, an alternate unsupervised technique is needed for the estimation of λ0-measure values. This study has developed such a technique by integrating the idea of distance correlation and Shannon entropy. In this technique, the two inputs required to estimate λ0-measure values, namely, the interdependence degrees and fuzzy densities are determined by utilizing the distance correlation measures and entropy weights, respectively. An evaluation to rank the websites owned by five different hospitals located in Sabah, Malaysia, was conducted to illustrate the usage of the technique. A similar evaluation was also performed with a few selected MADM techniques for comparison purposes, where the proposed technique is found to have produced the most consistent ranking. From the literature perspective, this study has contributed an alternate unsupervised technique that can estimate λ0-measure values without necessitating any additional data from the decision-makers, and at the same time can better capture the interdependencies held by the attributes.

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Section: Determining the Interdependence Degrees Using Distance Corrementioning

confidence: 99%

An Alternate Unsupervised Technique Based on Distance Correlation and Shannon Entropy to Estimate λ0-Fuzzy Measure

2020

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“…The term energy derives from Newton's notion of gravitational potential enegry which in turn is a function of the distance between two bodies. Energy statistics have drawn considerable attention recently, and besides the two-sample problem and monitoring have found applications in nponparametric analysis of variance and in testing for independence; see Rizzo et al (2010) and the reviews of Székely and Rizzo (2013) (which includes a nice historical account of the concept of energy in Statistics), Székely and Rizzo (2016) and Edelmann et al (2019).…”

Section: Computationsmentioning

confidence: 99%

Change-point methods for multivariate time-series: paired vectorial observations

2020

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We consider paired and two-sample break-detection procedures for vectorial observations and multivariate time series. The new methods involve L2-type criteria based on empirical characteristic functions and are easy to compute regardless of dimension. We obtain asymptotic results that allow for application of the methods to a wide range of settings involving on-line as well as retrospective circumstances with dependence between the two time series as well as with dependence within each series. In the ensuing Monte Carlo study the new detection methods are implemented by means of resampling procedures which are properly adapted to the type of data at hand, be it independent or paired, autoregressive or GARCH structured, medium or heavy-tailed. The new methods are also applied on a real dataset from the financial sector over a time period which includes the Brexit referendum. Keywords Change-point detection • Empirical characteristic function • Two-sample problem • Resampling procedures To the memory of Theophilos Cacoullos (1932-2020). Simos G. Meintanis-On sabbatical leave from the University of Athens.

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“…It should be mentioned that DCov has become a popular tool in independence testing and enjoys a number of extensions from the i.i.d. setting, such as for time-series and stochastic processes (see Székely and Rizzo (2009), Davis et al (2018), and the review by Edelmann et al (2020)), but also in abstract spaces by Lyons (2013); we also refer to the recent contribution by Shen et al (2020). However, distance covariance presupposes existence of moments which is not the case for our CF-based statistics.…”

Section: Connection With Energy Testsmentioning

confidence: 99%

Testing serial independence with functional data

Hlávka

Hušková

Meintanis

2020

TEST

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We consider tests of serial independence for a sequence of functional observations. The new methods are formulated as L2-type criteria based on empirical characteristic functions and are convenient from the computational point of view. We derive asymptotic normality of the proposed test statistics for both discretely and continuously observed functions. In a Monte Carlo study, we show that the new test is sensitive with respect to functional GARCH alternatives, investigate the choice of necessary tuning parameters, and demonstrate that critical values obtained by resampling lead to a test with good performance in any setup, whereas the asymptotic critical values may be recommended only for a sufficiently fine discretization grid. Finite-sample comparison with a distance (auto)covariance test criterion is also included, and the article concludes with application on a real data set.

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An Updated Literature Review of Distance Correlation and Its Applications to Time Series

Cited by 41 publications

References 93 publications

An Alternate Unsupervised Technique Based on Distance Correlation and Shannon Entropy to Estimate λ0-Fuzzy Measure

An Alternate Unsupervised Technique Based on Distance Correlation and Shannon Entropy to Estimate λ0-Fuzzy Measure

Change-point methods for multivariate time-series: paired vectorial observations

Testing serial independence with functional data

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