637 research outputs found
Long Memory and Volatility Clustering: is the empirical evidence consistent across stock markets?
Long memory and volatility clustering are two stylized facts frequently
related to financial markets. Traditionally, these phenomena have been studied
based on conditionally heteroscedastic models like ARCH, GARCH, IGARCH and
FIGARCH, inter alia. One advantage of these models is their ability to capture
nonlinear dynamics. Another interesting manner to study the volatility
phenomena is by using measures based on the concept of entropy. In this paper
we investigate the long memory and volatility clustering for the SP 500, NASDAQ
100 and Stoxx 50 indexes in order to compare the US and European Markets.
Additionally, we compare the results from conditionally heteroscedastic models
with those from the entropy measures. In the latter, we examine Shannon
entropy, Renyi entropy and Tsallis entropy. The results corroborate the
previous evidence of nonlinear dynamics in the time series considered.Comment: 8 pages; 2 figures; paper presented in APFA 6 conferenc
Long Memory and Volatility Clustering: is the empirical evidence consistent across stock markets?
Long memory and volatility clustering are two stylized facts frequently
related to financial markets. Traditionally, these phenomena have been studied
based on conditionally heteroscedastic models like ARCH, GARCH, IGARCH and
FIGARCH, inter alia. One advantage of these models is their ability to capture
nonlinear dynamics. Another interesting manner to study the volatility
phenomena is by using measures based on the concept of entropy. In this paper
we investigate the long memory and volatility clustering for the SP 500, NASDAQ
100 and Stoxx 50 indexes in order to compare the US and European Markets.
Additionally, we compare the results from conditionally heteroscedastic models
with those from the entropy measures. In the latter, we examine Shannon
entropy, Renyi entropy and Tsallis entropy. The results corroborate the
previous evidence of nonlinear dynamics in the time series considered.Comment: 8 pages; 2 figures; paper presented in APFA 6 conferenc
Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System
Peer reviewedPublisher PD
Use of the geometric mean as a statistic for the scale of the coupled Gaussian distributions
The geometric mean is shown to be an appropriate statistic for the scale of a
heavy-tailed coupled Gaussian distribution or equivalently the Student's t
distribution. The coupled Gaussian is a member of a family of distributions
parameterized by the nonlinear statistical coupling which is the reciprocal of
the degree of freedom and is proportional to fluctuations in the inverse scale
of the Gaussian. Existing estimators of the scale of the coupled Gaussian have
relied on estimates of the full distribution, and they suffer from problems
related to outliers in heavy-tailed distributions. In this paper, the scale of
a coupled Gaussian is proven to be equal to the product of the generalized mean
and the square root of the coupling. From our numerical computations of the
scales of coupled Gaussians using the generalized mean of random samples, it is
indicated that only samples from a Cauchy distribution (with coupling parameter
one) form an unbiased estimate with diminishing variance for large samples.
Nevertheless, we also prove that the scale is a function of the geometric mean,
the coupling term and a harmonic number. Numerical experiments show that this
estimator is unbiased with diminishing variance for large samples for a broad
range of coupling values.Comment: 17 pages, 5 figure
Entanglement Detection Using Majorization Uncertainty Bounds
Entanglement detection criteria are developed within the framework of the
majorization formulation of uncertainty. The primary results are two theorems
asserting linear and nonlinear separability criteria based on majorization
relations, the violation of which would imply entanglement. Corollaries to
these theorems yield infinite sets of scalar entanglement detection criteria
based on quasi-entropic measures of disorder. Examples are analyzed to probe
the efficacy of the derived criteria in detecting the entanglement of bipartite
Werner states. Characteristics of the majorization relation as a comparator of
disorder uniquely suited to information-theoretical applications are emphasized
throughout.Comment: 10 pages, 1 figur
Reduced perplexity: Uncertainty measures without entropy
Conference paper presented at Recent Advances in Info-Metrics, Washington, DC, 2014. Under review for a book chapter in "Recent innovations in info-metrics: a cross-disciplinary perspective on information and information processing" by Oxford University Press.A simple, intuitive approach to the assessment of probabilistic inferences is introduced. The Shannon information metrics are translated to the probability domain. The translation shows that the negative logarithmic score and the geometric mean are equivalent measures of the accuracy of a probabilistic inference. Thus there is both a quantitative reduction in perplexity as good inference algorithms reduce the uncertainty and a qualitative reduction due to the increased clarity between the original set of inferences and their average, the geometric mean. Further insight is provided by showing that the Renyi and Tsallis entropy functions translated to the probability domain are both the weighted generalized mean of the distribution. The generalized mean of probabilistic inferences forms a Risk Profile of the performance. The arithmetic mean is used to measure the decisiveness, while the -2/3 mean is used to measure the robustness
Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements
We derive an entropic uncertainty relation for generalized
positive-operator-valued measure (POVM) measurements via a direct-sum
majorization relation using Schur concavity of entropic quantities in a
finite-dimensional Hilbert space. Our approach provides a significant
improvement of the uncertainty bound compared with previous majorization-based
approaches [S. Friendland, V. Gheorghiu and G. Gour, Phys. Rev. Lett. 111,
230401 (2013); A. E. Rastegin and K. \.Zyczkowski, J. Phys. A, 49, 355301
(2016)], particularly by extending the direct-sum majorization relation first
introduced in [\L. Rudnicki, Z. Pucha{\l}a and K. \.{Z}yczkowski, Phys. Rev. A
89, 052115 (2014)]. We illustrate the usefulness of our uncertainty relations
by considering a pair of qubit observables in a two-dimensional system and
randomly chosen unsharp observables in a three-dimensional system. We also
demonstrate that our bound tends to be stronger than the generalized
Maassen--Uffink bound with an increase in the unsharpness effect. Furthermore,
we extend our approach to the case of multiple POVM measurements, thus making
it possible to establish entropic uncertainty relations involving more than two
observables
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