Auswahl der wissenschaftlichen Literatur zum Thema „Relation Skewness-Kurtosis“

We explore the cross-section of realized variance, skewness, and kurtosis for stock returns obtained from intraday data. We investigate the properties of the realized higher moments, and more importantly, examine relations between the realized moments and subsequent stock returns. We find evidence of a negative relation between realized skewness and next week’s returns. A strategy buying stocks in the lowest realized skewness quintile and selling stocks in the highest realized skewness quintile earns 0.79 percent per week a risk-adjusted basis. Our results on the realized skewness are robust to controls for various firm characteristics such as size and book-to-market. Little evidence exists that either the realized volatility or the realized kurtosis is significantly related to next week’s returns.

Due to many theoretical and practical shortcomings of the traditional CAPM model, this study aims at analyzing the CAPM with possible extensions. The analysis aims to know the empirical soundness of Conditional Higher Moment CAPM in emerging India’s capital market. The sample consists of 69 company’s daily stock price data from April 2004 to March 2019 from NSE 100. Panel data analysis is used on 21 cross-sections. The overall results show that when both up and down markets are incorporated separately, all three moments, namely, co-variance, co-skewness, and co-kurtosis, are priced during the normal Indian economy phase. Further, this study states that including higher moments (co-skewness and co-kurtosis) in the two-moment model provides symmetry in both the up and down markets. This is one of the first studies in the Indian Stock market explaining the variation in portfolio returns through panel data analysis by extending CAPM with conditional higher-order co-moments. The portfolio managers should consider skewness and kurtosis along with variance in constructing the optimal portfolios.

Abstract The thermodynamic uncertainty relation is a prominent result in stochastic thermodynamics that provides a bound on the fluctuations of any thermodynamic flux, also known as current, in terms of the average rate of entropy production. Such fluctuations are quantified by the second moment of the probability distribution of the current. The role of higher order standardized moments such as skewness and kurtosis remains largely unexplored. We analyze the skewness and kurtosis associated with the first passage time of thermodynamic currents within the framework of stochastic thermodynamics. We develop a method to evaluate higher order standardized moments associated with the first passage time of any current. For systems with a unicyclic network of states, we conjecture upper and lower bounds on skewness and kurtosis associated with entropy production. These bounds depend on the number of states and the thermodynamic force that drives the system out of equilibrium. We show that these bounds for skewness and kurtosis do not hold for multicyclic networks. We discuss the application of our results to infer an underlying network of states.

Abstract. In a recent paper (Chian et al., 2016) it was shown that magnetic reconnection at the interface region between two magnetic flux ropes is responsible for the genesis of interplanetary intermittent turbulence. The normalized third-order moment (skewness) and the normalized fourth-order moment (kurtosis) display a quadratic relation with a parabolic shape that is commonly observed in observational data from turbulence in fluids and plasmas, and is linked to non-Gaussian fluctuations due to coherent structures. In this paper we perform a detailed study of the relation between the skewness and the kurtosis of the modulus of the magnetic field |B| during a triple interplanetary magnetic flux rope event. In addition, we investigate the skewness–kurtosis relation of two-point differences of |B| for the same event. The parabolic relation displays scale dependence and is found to be enhanced during magnetic reconnection, rendering support for the generation of non-Gaussian coherent structures via rope–rope magnetic reconnection. Our results also indicate that a direct coupling between the scales of magnetic flux ropes and the scales within the inertial subrange occurs in the solar wind. Keywords. Space plasma physics (turbulence)

The power Lomax distribution due to Rady et al. (2016) is an alternative to and provides better fits for bladder cancer data (Lee and Wang, 2003) than the Lomax, exponential Lo- max, Weibull Lomax, extended Poisson Lomax and beta Lomax distributions. Exact explicit expressions as well as recurrence relations for the single and double (product) moments have been derived from the power Lomax distribution. These recurrence relations enable computation of the mean, variance, skewness and kurtosis of all order statistics for all sample sizes in a simple and efficient manner. By using these relation, the mean, variance, skewness and kurtosis of order statistics for sample sizes up to 5 for various values of shape and scale parameters are tabulated. Finally, remission times (in months) of bladder cancer patients have been analyzed to show how the proposed relations work in practice.

This paper explores whether the high or low ESG rating of a company is related to the level of its implied tail risk, measured on the basis of derivative data by implied skewness and implied kurtosis. Previous research suggests that the ESG rating of a company is indeed connected to some financial risk; however, often, only volatility is used as a risk measure. We examined the relation between ESG ratings and implied volatility, and explore the relation between ESG ratings and financial risk in more depth by looking into higher implied moments accessing financial tail risk. First, we found that higher ESG rated companies have a lower implied volatility connected with them, and exhibit more negative implied skewness and higher implied kurtosis. In other words, we observed a higher negative tail risk for higher ESG rated companies. However, on a midsized company data set, we found that higher ESG rated companies both have lower implied volatility, and exhibit less negative implied skewness and lower implied kurtosis. Hence, negative tail risk is typically lower for high ESG rated companies. Our study further investigated similar effects on individual environmental (E), social (S) and governance (G) scores of the involved companies. Second, we examined whether such a kind of trend exists for different sectors. Our results indicate that the influence of ESG ratings on implied volatility exhibits a similar trend, except for the industrial, information services, and real estate sectors, while for the materials, healthcare, and communication services sectors, the influence of ESG ratings on implied skewness and implied kurtosis is less pronounced. Moreover, the results show that the ESG ratings are correlated with implied moments for companies in consumer discretionary sectors.

The current empirical study attempts to analyze the impact of COVID-19 on the performance of the Indian stock market concerning two composite indices (BSE 500 and BSE Sensex) and eight sectoral indices of Bombay Stock Exchange (BSE) (Auto, Bankex, Consumer Durables, Capital Goods, Fast Moving Consumer Goods, Health Care, Information Technology, and Realty) of India, and compare the composite indices of India with three global indexes S&P 500, Nikkei 225, and FTSE 100. The daily data from January 2019 to May 2020 have been considered in this study. GLS regression has been applied to assess the impact of COVID-19 on the multiple measures of volatility, namely standard deviation, skewness, and kurtosis of all indices. All indices’ key findings show lower mean daily return than specific, negative returns in the crisis period compared to the pre-crisis period. The standard deviation of all the indices has gone up, the skewness has become negative, and the kurtosis values are exceptionally large. The relation between indices has increased during the crisis period. The Indian stock market depicts roughly the same standard deviation as the global markets but has higher negative skewness and higher positive kurtosis of returns, making the market seem more volatile.

Aims. We investigate the evolution of the one-point probability distribution function (PDF) of the dark matter density field and the evolution of its moments for fluctuations that are Gaussian in the linear regime. Methods. We performed numerical simulations of the evolution of the cosmic web for the conventional ΛCDM model. The simulations covered a wide range of box sizes L = 256 − 4000 h−1 Mpc, mass, and force resolutions, and epochs from very early moments z = 30 to the present moment z = 0. We calculated density fields with various smoothing lengths to determine the dependence of the density field on the smoothing scale. We calculated the PDF and its moments variance, skewness, and kurtosis. We determined the dependence of these parameters on the evolutionary epoch z, on the smoothing length Rt, and on the rms deviation of the density field σ using a cubic-cell and top-hat smoothing with kernels 0.4 h−1 Mpc ≤ Rt ≤ 32 h−1 Mpc. Results. We focus on the third (skewness S) and fourth (kurtosis K) moments of the distribution functions: their dependence on the smoothing scale Rt, the amplitude of the fluctuations σ, and the redshift z. Moments S and K, calculated for density fields at different cosmic epochs and smoothed with various scales, characterise the evolution of different structures of the web. Moments calculated with small-scale smoothing (Rt ≈ (1 − 4) h−1 Mpc) characterise the evolution of the web on cluster-type scales. Moments found with strong smoothing (Rt ≳ (5 − 15) h−1 Mpc) describe the evolution of the web on supercluster scales. During the evolution, the reduced skewness S3 = S/σ and reduced kurtosis S4 = K/σ2 present a complex behaviour: at a fixed redshift, curves of S3(σ) and S4(σ) steeply increase with σ at σ ≲ 1 and then flatten out and become constant at σ ≳ 2. When we fixed the smoothing scale Rt, the curves at large σ started to gradually decline after reaching the maximum at σ ≈ 2. We provide accurate fits for the evolution of S3, 4(σ, z). Skewness and kurtosis approach constant levels at early epochs S3(σ)≈3 and S4(σ)≈15. Conclusions. Most of the statistics of dark matter clustering (e.g. halo mass function or concentration-mass relation) are nearly universal: they mostly depend on the σ with a relatively modest correction to apparent dependence on the redshift. We find just the opposite for skewness and kurtosis: the dependence of the moments on the evolutionary epoch z and smoothing length Rt is very different. Together, they uniquely determine the evolution of S3, 4(σ). The evolution of S3 and S4 cannot be described by current theoretical approximations. The often used lognormal distribution function for the PDF fails to even qualitatively explain the shape and evolution of S3 and S4.

Digitization of carton’s dispersion is important for rubber researching. In statistics, kurtosis and skewness can been used to evaluate the dispersion, control chart can been used to decrease the influence of abnormal factors. The application of computer technology can finish calculating and showing of statistical data quickly and exactly. Digitization of distribution supplies more ways to research the relation between carton’s dispersion and rubber’s property.

Seismic excitations occur as mainshock-aftershock sequences (MS-AS) encompassing a strong event called mainshock with the largest magnitude in the set, or as earthquake swarms (ES) when a distinctive main event is absent. In regions as the gulf of Corinth, where active deformation is manifested with frequent seismicity bursts, it is important to distinguish MS-AS from ES for providing information on the physical process of earthquake generation and contribute to the seismic hazard assessment. For this purpose, a highly accurate local earthquake catalogue was compiled and an effort was made for clusters identification after establishing certain criteria based on spatio-temporal seismicity properties. The skewness and kurtosis of moment release history were calculated considering the normalized time of every event in a cluster since the starting time of the cluster and its seismic moment. For MS-AS we found large positive values for skewness and kurtosis contrary to ES that exhibit negative to low positive values for skewness and even lower values for kurtosis.In order to verify the classification of clusters, the b-value, the spatial size and the number of events of each cluster were examined. Finally, a scaling relation between the length of the rupture zone and magnitude derived for the MS-AS sequences.

Comprendre et prédire la dynamique de la biodiversité sous contraintes du changement global représente un défi scientifique majeur. Cependant, la réponse de la biodiversité au changement global est intrinsèquement complexe. En effet, les facteurs de changement en jeu n'affectent pas seulement la diversité des espèces et leur abondance, mais modifient également les interactions biotiques entre espèces, ce qui impacte l‘assemblage des communautés et leurs dynamiques. Dans ce contexte, l'étude de la diversité des traits fonctionnels pourrait permettre des avancées significatives car les traits reflètent la manière dont les espèces répondent et influencent leur environnement. Pour rendre l'approche fonctionnelle opérationnelle à l'étude de la complexité des systèmes écologiques, nous avons développé une démarche analytique novatrice qui repose sur l'étude des formes de distribution de traits. La forme des distributions de traits peut être caractérisée par une la relation entre la skewness et la kurtosis : la SKR. Plus précisément, nous avons développé deux indicateurs clés (Chapitre 1), dérivés de la SKR : le TADeve qui caractérise l'équitabilité fonctionnelle, et le TADstab qui caractérise la stabilité des distributions de traits.En nous appuyant sur les prairies permanentes comme modèle d'étude, nous avons mis en avant la pertinence de l'étude de l'équitabilité (TADeve) et de la stabilité (TADstab) des distributions de traits afin de dissocier l'influence de processus déterministes (p.ex. filtre de l'habitat, différentiation de niche) de la stochasticité inhérente aux systèmes écologiques (Chapitre 1). La mobilisation d'un jeu de données de suivi de prairies permanentes gérées de manière contrastée sur le long terme (17 ans), nous a permis de montrer que la dynamique des distributions de traits n'était pas aléatoire mais dépendante des pratiques de gestion (Chapitre 2). Les prairies gérées de manière intensive (haut niveau de fertilisation) sont associées à des distributions de traits instables et inéquitables. Ces résultats sont cohérents avec un scénario théorique du « filtre de l'habitat » et l'effet d'une compétition intense limitant la diversité. Dans le cas des prairies gérées de manière extensive (absence de fertilisation), les distributions de traits sont remarquablement équitables et stables. Ces résultats sont cohérents avec un scénario théorique de la « différenciation de niche » prédisant une coexistence stable d'espèces fonctionnellement contrastées. Par ailleurs, nous avons montré que l'arrêt de la fertilisation entraîne, en quelques années, une convergence vers des distributions de traits équitables et stables, favorisant ainsi le recrutement à long terme d'une flore prairiale riche et diversifiée. Nous montrons également que l'équitabilité et la stabilité des distributions de traits s'expliqueraient par l'émergence d'une complémentarité entre espèces dominantes et subordonnées permettant une stabilisation sur le long terme de l'assemblage fonctionnel et de toute la communauté végétale (Chapitre 3). Enfin, une étude comparative des patrons de diversité fonctionnelle, entre des communautés prairiales gérées et des communautés végétales naturelles, nous a permis de montrer que ces communautés partagent des organisations fonctionnelles similaires. L'observation de patrons communs dans le temps et dans l'espace suggère l'existence de règles générales déterminant à la fois l'assemblage, la diversité et la dynamique des communautés prairiales.En conclusion, l'approche SKR semble adaptée à l'étude de systèmes complexes dynamiques, tels que les systèmes écologiques en contexte de changement global. A l'ère de l'anthropocène, l'identification de règles générales d'assemblage basées sur les traits permettrait de concevoir des modes de gestion adaptés à la préservation et à la restauration de la biodiversité, ainsi qu'au maintien de la multifonctionnalité des écosystèmes
Understanding and predicting the dynamics of biodiversity under global change is a major scientific challenge. However, biodiversity responses to global change are inherently complex. Drivers of change not only affect species diversity and abundance but also alter biotic interactions between species, which may impact community assembly and dynamics. In this context, studying the diversity of functional traits within communities could lead to significant advances, as traits reflect how species respond to and influence their environment. To make the trait-based approach operational for the study of complex ecological systems, we developed an innovative analytical framework based on the study of the shapes of trait distributions. The shapes of trait distributions can be characterised by an inequality between the skewness and the kurtosis, the Skewness-Kurtosis Relationship (SKR). Using this inequality, we developed two key indicators (Chapter 1): the TADeve, which characterises the evenness of trait distributions, and the TADstab, which characterises the stability of trait distributions.Using permanent grasslands as a study model, we highlighted the relevance of studying the evenness (TADeve) and stability (TADstab) of trait distributions in order to disentangle the influence of deterministic processes (e.g. habitat filtering, niche differentiation), while accounting for the inherent stochasticity of ecological systems (Chapter 1). Using a long-term dataset of managed permanent grasslands (17-years), we demonstrated that the temporal variability of trait distributions was not random, but depended on management practices (Chapter 2). Intensively managed grasslands (high levels of fertilisation) are associated with unstable and uneven trait distributions. These results are consistent with predictions of the “habitat filtering” theory and the occurrence of intense competition between plant species that limit local diversity. Conversely, extensively managed grasslands (no fertilisation) were linked to remarkably even and stable trait distributions over time. Furthermore, we also showed that the cessation of fertilisation in extensively-managed grasslands led to a rapid convergence towards even and stable trait distributions, which promoted the long-term recruitment and persistence of a rich and diverse grassland flora. These findings are consistent with a theoretical scenario of niche differentiation, which predicts a stable coexistence among functionally contrasting species. Finally, we found that the high evenness and stability of trait distributions, in extensively managed grasslands, are explained by a functional complementarity between dominant and subordinate species, facilitating the long-term stabilisation of the functional assemblage and of the entire plant community (Chapter 3). Using observational data from various ecological context, we showed that semi-natural and natural plant communities shared a similar functional organisation. The observation of common functional patterns over space and time suggests the existence of general rules governing the assembly, diversity, and dynamics of plant communities.In conclusion, the SKR approach appears to be a suitable tool to study complex dynamic systems, such as ecological systems in the context of global change. In the Anthropocene era, identifying general assembly rules based on functional traits could enable the design of management methods adapted to the conservation and restoration of biodiversity, as well as the maintenance of ecosystem multifunctionality

The concept of emerging markets came to surface in early 1980 and constituted of only eight countries from the two continents of South America and Asia. The globalization of financial markets has since raised the importance of emerging capital markets. We take a quantitative approach to investigate the performance of emerging markets compared to developed markets. The aim of the study is to conclude if emerging markets offers investment value and if logic in portfolio theory can be used to improve the chance of creating a relatively better performing investment. Included markets in our study are Brazil, Russia, India, China, Colombia, Indonesia, Vietnam, Egypt, Turkey and South Africa. S&P 500 is our benchmark for developed market performance. Sample period is 2002-01-01 to 2011-12-31 and monthly return data, creating 120 data points on each index.   The weighting schemes used for the portfolios are min variance optimization, geographical location and high and low correlation. All investments are scored on performances in correlation to S&P 500, inflation adjusted growth, currency effect, Sharpe ratio, skewness and kurtosis. Rankings are done on the separate categories, on the individual overall ranking on only countries and one overall ranking on all investments. A brief overview of the overall ranking for all investments suggest that medium performing investments are overrepresented (12/20) and the low and high is underrepresented (3/20 and 5/20). Of note is that the min variance portfolio outperforms its components, the geographical portfolios have a wide range and the high correlated portfolio outperforms the low. The country to portfolio ratio over each grade suggests only a small skew of the results. There is no low scoring portfolio but the other two ratios are close to 50/50, suggesting that on average the portfolios create diversification benefits. Furthermore normality of returns seem to be violated and then the concept of volatility as a risk measure is significantly impaired also currency risk can be of high importance, currency effects ranged from -48% to 28.7%. Assuming non-normality seems more accurate than assuming normality; therefore we need to improve on volatility as a tool to measure risk. So one direction for further research we see a need is in the concept of volatility. The initial reason for this research came from small investors’ seemingly intuitive knowledge that emerging markets are a suitable investment option. We have concluded that they in fact are, therefore we suggest that a qualitative study is conducted to investigate this seemingly natural intuition.

Expected utility is introduced. Risk aversion and its equivalence with concavity of the utility function (Jensen’s inequality) are explained. The concepts of relative risk aversion, absolute risk aversion, and risk tolerance are introduced. Certainty equivalents are defined. Expected utility is shown to imply second‐order risk aversion. Linear risk tolerance (hyperbolic absolute risk aversion), cautiousness parameters, constant relative risk aversion, and constant absolute risk aversion are described. Decreasing absolute risk aversion is shown to imply a preference for positive skewness. Preferences for kurtosis are discussed. Conditional expectations are introduced, and the law of iterated expectations is explained. Risk averse investors are shown to dislike mean‐independent noise.

Abstract This article introduces a semiparametric autoregressive conditional hetero scedasticity (ARCH) model that has conditional first and second moments given by autoregressive moving average and ARCH parametric formulations but a conditional density that is assumed only to be sufficiently smooth to be approximated by a nonparametric density estimator. For several particular conditional densities, the relative efficiency of the quasi-maximum likelihood estimator is compared with maximum likelihood under correct specification. These potential efficiency gains for a fully adaptive procedure are compared in a Monte Carlo experiment with the observed gains from using the proposed semiparametric procedure, and it is found that the estimator captures a substantial proportion of the potential. The estimator is applied to daily stock returns from small firms that are found to exhibit conditional skewness and kurtosis and to the British pound to dollar exchange rate.

When the turbulent structures in the shear layer of high-speed jets travel at supersonic convective speeds relative to the ambient speed of sound, they radiate Mach waves that become the dominant component of the overall perceived noise. This is consistent with the OASPL in the far field reaching a maximum in same direction as the Mach wave angle. When the speed of the supersonic jet exceeds a certain level, the steepening of the wave-front in the near field produces a noise feature called “crackle.” Both pressure wave steepening and crackle cannot be recognized in the spectrum of the pressure signal, but in the temporal waveform of the pressure. The statistics of the pressure signal and its time derivative, particularly skewness, have become standard measures of crackle in heated supersonic jets. Previous studies showed that it is possible to reduce far-field pressure skewness with the implementation of notched and chevron nozzles, and to mitigate Mach Wave radiation with secondary flow techniques. In this paper, we investigate the effect of chevrons on the pressure and dP/dt high-order statistics of a Md = 1.5 converging-diverging round conical nozzle, both in the near and far fields. Cold and heated jets, To = 300 K and 600 K, are tested at over, design, and under-expanded conditions. Far-field results of the heated jet showed that chevrons effectively reduce elevated levels of skewness and kurtosis of the pressure and dP/dt. These reductions are remarkable especially around the Mach Wave angle, the region in which high-order statistics tend to propagate. Near-field results corroborated the effectiveness of chevrons in the skewness reduction.

This paper presents the influence of commanding parameters as load and relative sliding speed, on the surface characteristics. Tests were done on a roller-roller tribotester. There were studied the influence of load, relative sliding speed and lubricant on the skewness and the kurtosis of the surface profile, but also on common parameters such as Ra and Rz. Such a study may be used for selecting a suitable lubricant (especially grease), after testing it under severe conditions, close to the actual ones. Profilograms indicate that treated steel has a better tribological behavior, under the above-mentioned testing conditions, for a roller-roller system. When running at low temperatures, there were noticed gripping traces, pointed out in shape and size by profilograms recorded on the roller generatrix. For all testing conditions, the more viscous grease (UM185Li2 EP – multifunctional grease) had a better behavior as concerning the profile parameters of the roller surfaces, and it provides a probably almost continuous film between rollers thus, a good protection of the metallic surfaces, process also underlined by low values for the recorded friction moment. A comparative study of the surface topography, obtained under the same testing conditions, may do at least a qualitative hierarchy of the grease grades, which could give recommendations for selecting lubricants and durability improvement of actual tribosystems.